QuestionFind the hypotenuse $x$ of a right triangle with a base of 20 units and a height of 10 units. Round to the nearest hundredth.

Studdy Solution

STEP 1

Assumptions1. The triangle is a right triangle. . The length of the base is20 units.
3. The length of the height is10 units.
4. We are looking for the length of the hypotenuse $x$ .

STEP 2

We will use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
$x^2 = base^2 + height^2$

STEP 3

Now, plug in the given values for the base and the height to calculate the square of the hypotenuse.
$x^2 =20^2 +10^2$

STEP 4

Calculate the square of the hypotenuse.
$x^2 =400 +100 =500$

STEP 5

Now that we have the square of the hypotenuse, we can find the length of the hypotenuse by taking the square root of $x^2$ .
$x = \sqrt{x^2}$

STEP 6

Plug in the value for $x^2$ to calculate the length of the hypotenuse.
$x = \sqrt{500}$

STEP 7

Calculate the length of the hypotenuse.
$x = \sqrt{500} \approx22.36$ The length of the hypotenuse $x$ is approximately22.36 units, rounded to the nearest hundredth.

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QuestionFind the hypotenuse $x$ of a right triangle with a base of 20 units and a height of 10 units. Round to the nearest hundredth.

Studdy Solution

STEP 1

Assumptions1. The triangle is a right triangle. . The length of the base is20 units.
3. The length of the height is10 units.
4. We are looking for the length of the hypotenuse $x$ .

STEP 2

We will use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
$x^2 = base^2 + height^2$

STEP 3

Now, plug in the given values for the base and the height to calculate the square of the hypotenuse.
$x^2 =20^2 +10^2$

STEP 4

Calculate the square of the hypotenuse.
$x^2 =400 +100 =500$

STEP 5

Now that we have the square of the hypotenuse, we can find the length of the hypotenuse by taking the square root of $x^2$ .
$x = \sqrt{x^2}$

STEP 6

Plug in the value for $x^2$ to calculate the length of the hypotenuse.
$x = \sqrt{500}$

STEP 7

Calculate the length of the hypotenuse.
$x = \sqrt{500} \approx22.36$ The length of the hypotenuse $x$ is approximately22.36 units, rounded to the nearest hundredth.

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QuestionFind the hypotenuse xxx of a right triangle with a base of 20 units and a height of 10 units. Round to the nearest hundredth.

Studdy Solution

STEP 1

Assumptions1. The triangle is a right triangle. . The length of the base is20 units.3. The length of the height is10 units.4. We are looking for the length of the hypotenuse xxx.

STEP 2

We will use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.x2=base2+height2x^2 = base^2 + height^2x2=base2+height2

STEP 3

Now, plug in the given values for the base and the height to calculate the square of the hypotenuse.x2=202+102x^2 =20^2 +10^2x2=202+102

STEP 4

Calculate the square of the hypotenuse.x2=400+100=500x^2 =400 +100 =500x2=400+100=500

STEP 5

Now that we have the square of the hypotenuse, we can find the length of the hypotenuse by taking the square root of x2x^2x2.x=x2x = \sqrt{x^2}x=x2​

STEP 6

Plug in the value for x2x^2x2 to calculate the length of the hypotenuse.x=500x = \sqrt{500}x=500​

STEP 7

Calculate the length of the hypotenuse.x=500≈22.36x = \sqrt{500} \approx22.36x=500​≈22.36The length of the hypotenuse xxx is approximately22.36 units, rounded to the nearest hundredth.

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

QuestionFind the hypotenuse $x$ of a right triangle with a base of 20 units and a height of 10 units. Round to the nearest hundredth.

Assumptions1. The triangle is a right triangle. . The length of the base is20 units.
3. The length of the height is10 units.
4. We are looking for the length of the hypotenuse $x$ .

We will use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
$x^2 = base^2 + height^2$

Now, plug in the given values for the base and the height to calculate the square of the hypotenuse.
$x^2 =20^2 +10^2$

Calculate the square of the hypotenuse.
$x^2 =400 +100 =500$

Now that we have the square of the hypotenuse, we can find the length of the hypotenuse by taking the square root of $x^2$ .
$x = \sqrt{x^2}$

Plug in the value for $x^2$ to calculate the length of the hypotenuse.
$x = \sqrt{500}$

Calculate the length of the hypotenuse.
$x = \sqrt{500} \approx22.36$ The length of the hypotenuse $x$ is approximately22.36 units, rounded to the nearest hundredth.