Question

for the following right triangle, find the side length x. 35, 12, x (right triangle with legs 35 and 12, hypotenuse 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 \( a \), \( b \) are the other two sides. Here, \( a = 35 \), \( b = 12 \), and \( x \) is the hypotenuse. So we have \( x^2 = 35^2 + 12^2 \).

Step2: Calculate the squares

First, calculate \( 35^2 = 1225 \) and \( 12^2 = 144 \). Then add them together: \( 1225 + 144 = 1369 \).

Step3: Find the square root

Now, take the square root of 1369 to find \( x \). Since \( \sqrt{1369} = 37 \), we get \( x = 37 \).

Answer:

\( x = 37 \)