Math  /  Geometry

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

Studdy Solution

STEP 1

1. The triangle is a right triangle.
2. The sides labeled 12 and 5 are the legs of the triangle.
3. The hypotenuse is labeled x x .

STEP 2

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

STEP 3

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

STEP 4

Substitute the known values into the Pythagorean Theorem. Here, a=5 a = 5 , b=12 b = 12 , and c=x c = x :
x2=52+122 x^2 = 5^2 + 12^2

STEP 5

Calculate the squares of the known side lengths:
x2=25+144 x^2 = 25 + 144

STEP 6

Add the results to find the value of x2 x^2 :
x2=169 x^2 = 169

STEP 7

Solve for x x by taking the square root of both sides:
x=169 x = \sqrt{169}

STEP 8

Calculate the square root:
x=13 x = 13
The side length x x is:
13 \boxed{13}

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