Question

Which of the following measurements could be the side lengths of a right triangle?
A.
36 in, 54 in, 60 in
B.
36 in, 48 in, 72 in
C.
30 in, 48 in, 60 in
D.
36 in, 48 in, 60 in

Answer 1

To determine which sets of measurements could represent the side lengths of a right triangle, we can use the Pythagorean theorem, which states that for a right triangle with sides of lengths \(a\), \(b\), and hypotenuse \(c\), the following holds:

\[
a^2 + b^2 = c^2
\]

We'll check each option assuming the largest number is the hypotenuse.

### Option A: \(36\), \(54\), \(60\)
\[
36^2 + 54^2 = 1296 + 2916 = 4212
\]
\[
60^2 = 3600
\]
Since \(4212 \neq 3600\), this is not a right triangle.

### Option B: \(36\), \(48\), \(72\)
\[
36^2 + 48^2 = 1296 + 2304 = 3600
\]
\[
72^2 = 5184
\]
Since \(3600 \neq 5184\), this is not a right triangle.

### Option C: \(30\), \(48\), \(60\)
\[
30^2 + 48^2 = 900 + 2304 = 3204
\]
\[
60^2 = 3600
\]
Since \(3204 \neq 3600\), this is not a right triangle.

### Option D: \(36\), \(48\), \(60\)
\[
36^2 + 48^2 = 1296 + 2304 = 3600
\]
\[
60^2 = 3600
\]
Since \(3600 = 3600\), this is a right triangle.

In conclusion, the only set of measurements that could be the side lengths of a right triangle is:

**D. \(36\) in, \(48\) in, \(60\) in**.