Math / Geometry

QuestionFor the following right triangle, find the side length $x$ .

Studdy Solution

STEP 1

1. The triangle is a right triangle.
2. The sides labeled 9 and 12 are the legs of the triangle.
3. The side labeled $x$ is the hypotenuse.

STEP 2

1. Identify the Pythagorean Theorem.
2. Substitute the known values into the theorem.
3. Solve for $x$ .

STEP 3

Recall the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse ( $c$ ) is equal to the sum of the squares of the lengths of the other two sides ( $a$ and $b$ ):
$c^2 = a^2 + b^2$

STEP 4

Substitute the known side lengths into the Pythagorean Theorem. Here, $a = 9$ , $b = 12$ , and $c = x$ .
$x^2 = 9^2 + 12^2$

STEP 5

Calculate the squares of the known side lengths:
$x^2 = 81 + 144$

STEP 6

Add the results to find the value of $x^2$ :
$x^2 = 225$

STEP 7

Solve for $x$ by taking the square root of both sides:
$x = \sqrt{225}$

STEP 8

Evaluate the square root:
$x = 15$
The side length $x$ is:
$\boxed{15}$

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QuestionFor the following right triangle, find the side length $x$ .

Studdy Solution

STEP 1

1. The triangle is a right triangle.
2. The sides labeled 9 and 12 are the legs of the triangle.
3. The side labeled $x$ is the hypotenuse.

STEP 2

1. Identify the Pythagorean Theorem.
2. Substitute the known values into the theorem.
3. Solve for $x$ .

STEP 3

Recall the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse ( $c$ ) is equal to the sum of the squares of the lengths of the other two sides ( $a$ and $b$ ):
$c^2 = a^2 + b^2$

STEP 4

Substitute the known side lengths into the Pythagorean Theorem. Here, $a = 9$ , $b = 12$ , and $c = x$ .
$x^2 = 9^2 + 12^2$

STEP 5

Calculate the squares of the known side lengths:
$x^2 = 81 + 144$

STEP 6

Add the results to find the value of $x^2$ :
$x^2 = 225$

STEP 7

Solve for $x$ by taking the square root of both sides:
$x = \sqrt{225}$

STEP 8

Evaluate the square root:
$x = 15$
The side length $x$ is:
$\boxed{15}$

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QuestionFor the following right triangle, find the side length xxx.

Studdy Solution

STEP 1

1. The triangle is a right triangle.2. The sides labeled 9 and 12 are the legs of the triangle.3. The side labeled x x x is the hypotenuse.

STEP 2

1. Identify the Pythagorean Theorem.2. Substitute the known values into the theorem.3. Solve for x x x.

STEP 3

Recall the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (c c c) is equal to the sum of the squares of the lengths of the other two sides (a a a and b b b):c2=a2+b2 c^2 = a^2 + b^2 c2=a2+b2

STEP 4

Substitute the known side lengths into the Pythagorean Theorem. Here, a=9 a = 9 a=9, b=12 b = 12 b=12, and c=x c = x c=x.x2=92+122 x^2 = 9^2 + 12^2 x2=92+122

STEP 5

Calculate the squares of the known side lengths:x2=81+144 x^2 = 81 + 144 x2=81+144

STEP 6

Add the results to find the value of x2 x^2 x2:x2=225 x^2 = 225 x2=225

STEP 7

Solve for x x x by taking the square root of both sides:x=225 x = \sqrt{225} x=225​

STEP 8

Evaluate the square root:x=15 x = 15 x=15 The side length x x x is:15 \boxed{15} 15​

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QuestionFor the following right triangle, find the side length $x$ .

1. The triangle is a right triangle.
2. The sides labeled 9 and 12 are the legs of the triangle.
3. The side labeled $x$ is the hypotenuse.

1. Identify the Pythagorean Theorem.
2. Substitute the known values into the theorem.
3. Solve for $x$ .

Recall the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse ( $c$ ) is equal to the sum of the squares of the lengths of the other two sides ( $a$ and $b$ ):
$c^2 = a^2 + b^2$

Substitute the known side lengths into the Pythagorean Theorem. Here, $a = 9$ , $b = 12$ , and $c = x$ .
$x^2 = 9^2 + 12^2$

Calculate the squares of the known side lengths:
$x^2 = 81 + 144$

Add the results to find the value of $x^2$ :
$x^2 = 225$

Solve for $x$ by taking the square root of both sides:
$x = \sqrt{225}$

Evaluate the square root:
$x = 15$
The side length $x$ is:
$\boxed{15}$