Math / Geometry

QuestionUnit 2 Corrections Name Cailyn. Travis
Question \#6 Lukas is walking around the edge of the playground shown. If each square represents 1 unit, how far will Lukas have walked when he finishes one loop around the playground? Round to the nearest unit, if necessary. $\qquad$ units $\begin{array}{l} A=(2,7) \\ B=(2,15) \\ C=(17,7) \end{array}$

Studdy Solution

STEP 1

What is this asking? How long is the perimeter of this triangle on the grid, where each square is one unit? Watch out! Don't forget to add all three sides, and make sure you calculate the length of the slanted side correctly!

STEP 2

1. Find the length of side AB.
2. Find the length of side AC.
3. Find the length of side BC.
4. Calculate the total distance.

STEP 3

Alright, let's start with side AB!
It's a vertical line, so we can just subtract the y-coordinates.
The y-coordinate of point B is $15$ and the y-coordinate of point A is $7$ .

STEP 4

So, the length of AB is $15 - 7 = \mathbf{8}$ units.
Awesome!

STEP 5

Next up, side AC.
This one's horizontal, so we subtract the x-coordinates.
Point C has an x-coordinate of $17$ , and point A has an x-coordinate of $2$ .

STEP 6

So, AC's length is $17 - 2 = \mathbf{15}$ units.
Fantastic!

STEP 7

Now for the tricky part, the slanted side BC!
We'll use the Pythagorean theorem: $a^2 + b^2 = c^2$ , where a and b are the legs and c is the hypotenuse.
We can think of the horizontal and vertical distances between B and C as the legs of a right triangle.

STEP 8

The horizontal distance is the same as the length of AC, which we already found: $\mathbf{15}$ units.
The vertical distance is the same as the length of AB, which we also found: $\mathbf{8}$ units.

STEP 9

Plugging these values into the Pythagorean theorem, we get $15^2 + 8^2 = c^2$ .
This simplifies to $225 + 64 = c^2$ , which means $289 = c^2$ .

STEP 10

Taking the square root of both sides gives us $c = \sqrt{289} = \mathbf{17}$ units.
So, the length of BC is $\mathbf{17}$ units.
Perfect!

STEP 11

Almost there!
To find the total distance Lukas walks, we add the lengths of all three sides: AB + AC + BC.

STEP 12

We found that AB is $\mathbf{8}$ units, AC is $\mathbf{15}$ units, and BC is $\mathbf{17}$ units.
Adding those up, we get $8 + 15 + 17 = \mathbf{40}$ units.

STEP 13

Lukas will have walked $\mathbf{40}$ units after one loop around the playground.

Was this helpful?

Studdy Solution

STEP 1

What is this asking? How long is the perimeter of this triangle on the grid, where each square is one unit? Watch out! Don't forget to add all three sides, and make sure you calculate the length of the slanted side correctly!

STEP 2

1. Find the length of side AB.
2. Find the length of side AC.
3. Find the length of side BC.
4. Calculate the total distance.

STEP 3

Alright, let's start with side AB!
It's a vertical line, so we can just subtract the y-coordinates.
The y-coordinate of point B is $15$ and the y-coordinate of point A is $7$ .

STEP 4

So, the length of AB is $15 - 7 = \mathbf{8}$ units.
Awesome!

STEP 5

Next up, side AC.
This one's horizontal, so we subtract the x-coordinates.
Point C has an x-coordinate of $17$ , and point A has an x-coordinate of $2$ .

STEP 6

So, AC's length is $17 - 2 = \mathbf{15}$ units.
Fantastic!

STEP 7

Now for the tricky part, the slanted side BC!
We'll use the Pythagorean theorem: $a^2 + b^2 = c^2$ , where a and b are the legs and c is the hypotenuse.
We can think of the horizontal and vertical distances between B and C as the legs of a right triangle.

STEP 8

The horizontal distance is the same as the length of AC, which we already found: $\mathbf{15}$ units.
The vertical distance is the same as the length of AB, which we also found: $\mathbf{8}$ units.

STEP 9

Plugging these values into the Pythagorean theorem, we get $15^2 + 8^2 = c^2$ .
This simplifies to $225 + 64 = c^2$ , which means $289 = c^2$ .

STEP 10

Taking the square root of both sides gives us $c = \sqrt{289} = \mathbf{17}$ units.
So, the length of BC is $\mathbf{17}$ units.
Perfect!

STEP 11

Almost there!
To find the total distance Lukas walks, we add the lengths of all three sides: AB + AC + BC.

STEP 12

We found that AB is $\mathbf{8}$ units, AC is $\mathbf{15}$ units, and BC is $\mathbf{17}$ units.
Adding those up, we get $8 + 15 + 17 = \mathbf{40}$ units.

STEP 13

Lukas will have walked $\mathbf{40}$ units after one loop around the playground.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

What is this asking? How long is the perimeter of this triangle on the grid, where each square is one unit? Watch out! Don't forget to add all three sides, and make sure you calculate the length of the slanted side correctly!

STEP 2

1. Find the length of side AB.2. Find the length of side AC.3. Find the length of side BC.4. Calculate the total distance.

STEP 3

Alright, let's **start** with side AB!It's a vertical line, so we can just subtract the y-coordinates.The y-coordinate of point B is 151515 and the y-coordinate of point A is 777.

STEP 4

So, the length of AB is 15−7=815 - 7 = \mathbf{8}15−7=8 units.Awesome!

STEP 5

Next up, side AC.This one's horizontal, so we subtract the x-coordinates.Point C has an x-coordinate of 171717, and point A has an x-coordinate of 222.

STEP 6

So, AC's length is 17−2=1517 - 2 = \mathbf{15}17−2=15 units.Fantastic!

STEP 7

Now for the tricky part, the slanted side BC!We'll use the **Pythagorean theorem**: a2+b2=c2a^2 + b^2 = c^2a2+b2=c2, where *a* and *b* are the legs and *c* is the hypotenuse.We can think of the horizontal and vertical distances between B and C as the legs of a right triangle.

STEP 8

The horizontal distance is the same as the length of AC, which we already found: 15\mathbf{15}15 units.The vertical distance is the same as the length of AB, which we also found: 8\mathbf{8}8 units.

STEP 9

Plugging these values into the Pythagorean theorem, we get 152+82=c215^2 + 8^2 = c^2152+82=c2.This simplifies to 225+64=c2225 + 64 = c^2225+64=c2, which means 289=c2289 = c^2289=c2.

STEP 10

Taking the square root of both sides gives us c=289=17c = \sqrt{289} = \mathbf{17}c=289​=17 units.So, the length of BC is 17\mathbf{17}17 units.Perfect!

STEP 11

Almost there!To find the total distance Lukas walks, we add the lengths of all three sides: AB + AC + BC.

STEP 12

We found that AB is 8\mathbf{8}8 units, AC is 15\mathbf{15}15 units, and BC is 17\mathbf{17}17 units.Adding those up, we get 8+15+17=408 + 15 + 17 = \mathbf{40}8+15+17=40 units.

STEP 13

Lukas will have walked 40\mathbf{40}40 units after one loop around the playground.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Find the length of side AB.
2. Find the length of side AC.
3. Find the length of side BC.
4. Calculate the total distance.

Alright, let's start with side AB!
It's a vertical line, so we can just subtract the y-coordinates.
The y-coordinate of point B is $15$ and the y-coordinate of point A is $7$ .

So, the length of AB is $15 - 7 = \mathbf{8}$ units.
Awesome!

Next up, side AC.
This one's horizontal, so we subtract the x-coordinates.
Point C has an x-coordinate of $17$ , and point A has an x-coordinate of $2$ .

So, AC's length is $17 - 2 = \mathbf{15}$ units.
Fantastic!

Now for the tricky part, the slanted side BC!
We'll use the Pythagorean theorem: $a^2 + b^2 = c^2$ , where a and b are the legs and c is the hypotenuse.
We can think of the horizontal and vertical distances between B and C as the legs of a right triangle.

The horizontal distance is the same as the length of AC, which we already found: $\mathbf{15}$ units.
The vertical distance is the same as the length of AB, which we also found: $\mathbf{8}$ units.

Plugging these values into the Pythagorean theorem, we get $15^2 + 8^2 = c^2$ .
This simplifies to $225 + 64 = c^2$ , which means $289 = c^2$ .

Taking the square root of both sides gives us $c = \sqrt{289} = \mathbf{17}$ units.
So, the length of BC is $\mathbf{17}$ units.
Perfect!

Almost there!
To find the total distance Lukas walks, we add the lengths of all three sides: AB + AC + BC.

We found that AB is $\mathbf{8}$ units, AC is $\mathbf{15}$ units, and BC is $\mathbf{17}$ units.
Adding those up, we get $8 + 15 + 17 = \mathbf{40}$ units.

Lukas will have walked $\mathbf{40}$ units after one loop around the playground.