Question

for the following right triangle, find the side length x. image of a right triangle with horizontal leg 12, vertical leg 35, right angle at their intersection, and hypotenuse labeled x

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, the Pythagorean theorem states that \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse (the side opposite the right angle) and \( a \) and \( b \) are the other two sides. Here, \( a = 12 \), \( b = 35 \), and \( x \) is the hypotenuse. So we have \( 12^2 + 35^2 = x^2 \).

Step2: Calculate the squares

First, calculate \( 12^2 = 144 \) and \( 35^2 = 1225 \). Then add them together: \( 144 + 1225 = x^2 \).

Step3: Sum the values

\( 144 + 1225 = 1369 \), so \( x^2 = 1369 \).

Step4: Take the square root

To find \( x \), take the square root of both sides: \( x = \sqrt{1369} \).

Step5: Evaluate the square root

\( \sqrt{1369} = 37 \) since \( 37 \times 37 = 1369 \).

Answer:

37