Question

for the following right triangle, find the side length x. round your answer to the nearest hundredth.

Explanation:

Step1: Apply Pythagorean theorem

In a right triangle, \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse, and \( a, b \) are the legs. Here, hypotenuse \( c = 20 \), one leg \( b = 12 \), and the other leg is \( x \). So, \( x^2 + 12^2 = 20^2 \).

Step2: Solve for \( x^2 \)

Calculate \( 12^2 = 144 \) and \( 20^2 = 400 \). Then \( x^2 = 400 - 144 = 256 \)? Wait, no, wait. Wait, no, if the right angle is between \( x \) and 12, then hypotenuse is 20. So \( x^2 + 12^2 = 20^2 \). Wait, \( 20^2 - 12^2 = x^2 \). \( 400 - 144 = 256 \)? Wait, no, 400 - 144 is 256? Wait, 400 - 100 is 300, minus 44 is 256. Then \( x = \sqrt{256} \)? Wait, no, that's 16. Wait, but maybe I misread the triangle. Wait, the right angle is at the top, so the two legs are \( x \) and 12, hypotenuse 20. So Pythagorean theorem: \( x^2 + 12^2 = 20^2 \). So \( x^2 = 20^2 - 12^2 = 400 - 144 = 256 \). Then \( x = \sqrt{256} = 16.00 \)? Wait, but that's a perfect square. Wait, maybe I made a mistake. Wait, 12-16-20 is a Pythagorean triple (3-4-5 scaled by 4: 12=34, 16=44, 20=5*4). So yes, \( x = 16.00 \).

Answer:

16.00