Question

A right triangle can be formed using three sides having lengths 18 inches, 24 inches, and
Responses
A 12 inches.12 inches.
B 15 inches.15 inches.
C 16 inches.16 inches.
D 28 inches.28 inches.
E 30 inches.

Answer 1

To determine which of the given lengths can form a right triangle with the other two sides (18 inches and 24 inches), we can use the Pythagorean theorem, which states that for a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Let's denote the lengths we have:
- a = 18 inches
- b = 24 inches
- c = length of the unknown side

The possible lengths we can test (from the options) are 12 inches, 15 inches, 16 inches, 28 inches, and 30 inches.

We will check if any of these can be the hypotenuse or one of the legs, ensuring the Pythagorean theorem holds true.

1. Test if 12 inches can work:
- If 12 is one of the legs, check:
\[
18^2 + 12^2 = 324 + 144 = 468 \quad (not\ a\ perfect\ square)
\]

2. Test if 15 inches can work:
- If 15 is one of the legs, check:
\[
18^2 + 15^2 = 324 + 225 = 549 \quad (not\ a\ perfect\ square)
\]

3. Test if 16 inches can work:
- If 16 is one of the legs, check:
\[
18^2 + 16^2 = 324 + 256 = 580 \quad (not\ a\ perfect\ square)
\]

4. Test if 28 inches can work:
- If 28 is the hypotenuse, check:
\[
18^2 + 24^2 = 324 + 576 = 900
\]
\[
28^2 = 784 \quad (not\ equal)
\]

5. Test if 30 inches can work:
- If 30 is the hypotenuse, check:
\[
18^2 + 24^2 = 324 + 576 = 900
\]
\[
30^2 = 900 \quad (equal)
\]

So, if the sides are 18 inches, 24 inches, and 30 inches, they do satisfy the Pythagorean theorem.

Thus, the answer is:

**E 30 inches.**