College

The side lengths of a right triangle are 13.5 yards and 60 yards. What is the length of the hypotenuse in yards?

A. 61.5 yd
B. 46.5 yd
C. 58.5 yd
D. 73.5 yd

Answer :

To find the length of the hypotenuse in a right triangle, we use the Pythagorean theorem. The theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The formula is:
[tex]\[ c^2 = a^2 + b^2 \][/tex]

where:
- [tex]\( c \)[/tex] is the hypotenuse,
- [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are the other two sides.

For this problem, we are given:
- One side, [tex]\( a = 13.5 \)[/tex] yards,
- Another side, [tex]\( b = 60 \)[/tex] yards.

Now, let's find the hypotenuse [tex]\( c \)[/tex]:

1. Square both of the given sides:
[tex]\[
a^2 = (13.5)^2 = 182.25
\][/tex]
[tex]\[
b^2 = (60)^2 = 3600
\][/tex]

2. Add the results:
[tex]\[
a^2 + b^2 = 182.25 + 3600 = 3782.25
\][/tex]

3. Take the square root of the sum to find the hypotenuse:
[tex]\[
c = \sqrt{3782.25} \approx 61.5
\][/tex]

Therefore, the length of the hypotenuse is approximately [tex]\( 61.5 \)[/tex] yards. So, the correct answer is 61.5 yards.