Question

to ensure right angles at the corners of a collection site, use the pythagorean theorem to find the hypotenuse of the right triangle formed by side a (9 meters, from corner x to corner z) and side b (12 meters, from corner x to corner y). the length of the hypotenuse, ______, should fit the distance between corner y and corner z if the corners are 90 degrees.
options:
a. 5 meters
b. 16 meters
c. 15 meters
d. 21 meters

Explanation:

Step1: Identify the sides of the right triangle

We have a right triangle with legs \( a = 9 \) meters and \( b = 12 \) meters. The Pythagorean theorem is \( c=\sqrt{a^{2}+b^{2}} \), where \( c \) is the hypotenuse.

Step2: Calculate \( a^{2} \) and \( b^{2} \)

\( a^{2}=9^{2} = 81 \), \( b^{2}=12^{2}=144 \)

Step3: Sum the squares

\( a^{2}+b^{2}=81 + 144=225 \)

Step4: Take the square root

\( c=\sqrt{225}=15 \) meters

Answer:

c. 15 meters