Math / Geometry

Question2. Find the perimeter of a square if the length of its diagonal is 16 cm. Round to the nearest tenth.
A. 512.0 cm B. 45.3 cm C. 128.0 cm D. 90.5 cm
3. Three checkpoints X, Y, and Z are placed in the ocean to mark a sailboat race. Contestants start at X, sail to checkpoint Y and Z, and then return to checkpoint X. The location of the checkpoints and the racecourse are shown below.
$2.8$ miles $40^\circ$ $56^\circ$
What is the distance between checkpoint X and checkpoint Z to the nearest tenth of a mile?

Studdy Solution

STEP 1

What is this asking? If a square's diagonal is $16$ cm, what's its perimeter? Watch out! Don't mix up the diagonal and the side!

STEP 2

1. Find the side length
2. Calculate the perimeter

STEP 3

We know the diagonal of our square is $16$ cm.
Let's call the side length $s$ .
Since it's a square, all sides are equal!

STEP 4

A square's diagonal cuts it into two right triangles.
We can use the Pythagorean theorem: $a^2 + b^2 = c^2$ .
Here, $a$ and $b$ are the sides ( $s$ ), and $c$ is the diagonal ( $16$ ).

STEP 5

So, we have $s^2 + s^2 = 16^2$ , which simplifies to $2s^2 = 256$ .

STEP 6

Divide both sides by $2$ to get $s^2 = 128$ .

STEP 7

Now, take the square root of both sides to find $s = \sqrt{128} \approx 11.31$ .
So, the side length is approximately $11.31$ cm.

STEP 8

A square has four equal sides.
The perimeter is just the sum of all sides.

STEP 9

With a side length of approximately $11.31$ cm, the perimeter is $4 \cdot 11.31 = 45.24$ cm.

STEP 10

Rounding to the nearest tenth gives us $45.3$ cm.

STEP 11

The perimeter of the square is approximately $45.3$ cm.
So the answer is B.

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Studdy Solution

STEP 1

What is this asking? If a square's diagonal is $16$ cm, what's its perimeter? Watch out! Don't mix up the diagonal and the side!

STEP 2

1. Find the side length
2. Calculate the perimeter

STEP 3

We know the diagonal of our square is $16$ cm.
Let's call the side length $s$ .
Since it's a square, all sides are equal!

STEP 4

A square's diagonal cuts it into two right triangles.
We can use the Pythagorean theorem: $a^2 + b^2 = c^2$ .
Here, $a$ and $b$ are the sides ( $s$ ), and $c$ is the diagonal ( $16$ ).

STEP 5

So, we have $s^2 + s^2 = 16^2$ , which simplifies to $2s^2 = 256$ .

STEP 6

Divide both sides by $2$ to get $s^2 = 128$ .

STEP 7

Now, take the square root of both sides to find $s = \sqrt{128} \approx 11.31$ .
So, the side length is approximately $11.31$ cm.

STEP 8

A square has four equal sides.
The perimeter is just the sum of all sides.

STEP 9

With a side length of approximately $11.31$ cm, the perimeter is $4 \cdot 11.31 = 45.24$ cm.

STEP 10

Rounding to the nearest tenth gives us $45.3$ cm.

STEP 11

The perimeter of the square is approximately $45.3$ cm.
So the answer is B.

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Studdy Solution

STEP 1

What is this asking? If a square's diagonal is 161616 cm, what's its perimeter? Watch out! Don't mix up the diagonal and the side!

STEP 2

1. Find the side length2. Calculate the perimeter

STEP 3

We know the **diagonal** of our square is 161616 cm.Let's call the **side length** sss.Since it's a square, all sides are equal!

STEP 4

A square's diagonal cuts it into two **right triangles**.We can use the **Pythagorean theorem**: a2+b2=c2a^2 + b^2 = c^2a2+b2=c2.Here, aaa and bbb are the sides (sss), and ccc is the diagonal (161616).

STEP 5

So, we have s2+s2=162s^2 + s^2 = 16^2s2+s2=162, which simplifies to 2s2=2562s^2 = 2562s2=256.

STEP 6

**Divide both sides by** 222 to get s2=128s^2 = 128s2=128.

STEP 7

Now, **take the square root of both sides** to find s=128≈11.31s = \sqrt{128} \approx 11.31s=128​≈11.31.So, the **side length** is approximately **11.3111.3111.31 cm**.

STEP 8

A square has **four equal sides**.The **perimeter** is just the sum of all sides.

STEP 9

With a **side length** of approximately 11.3111.3111.31 cm, the **perimeter** is 4⋅11.31=45.244 \cdot 11.31 = 45.244⋅11.31=45.24 cm.

STEP 10

Rounding to the **nearest tenth** gives us **45.345.345.3 cm**.

STEP 11

The perimeter of the square is approximately 45.345.345.3 cm.So the answer is B.

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What is this asking? If a square's diagonal is $16$ cm, what's its perimeter? Watch out! Don't mix up the diagonal and the side!

1. Find the side length
2. Calculate the perimeter

We know the diagonal of our square is $16$ cm.
Let's call the side length $s$ .
Since it's a square, all sides are equal!

A square's diagonal cuts it into two right triangles.
We can use the Pythagorean theorem: $a^2 + b^2 = c^2$ .
Here, $a$ and $b$ are the sides ( $s$ ), and $c$ is the diagonal ( $16$ ).

So, we have $s^2 + s^2 = 16^2$ , which simplifies to $2s^2 = 256$ .

Divide both sides by $2$ to get $s^2 = 128$ .

Now, take the square root of both sides to find $s = \sqrt{128} \approx 11.31$ .
So, the side length is approximately $11.31$ cm.

A square has four equal sides.
The perimeter is just the sum of all sides.

With a side length of approximately $11.31$ cm, the perimeter is $4 \cdot 11.31 = 45.24$ cm.

Rounding to the nearest tenth gives us $45.3$ cm.

The perimeter of the square is approximately $45.3$ cm.
So the answer is B.