The hypotenuse (side C) of a triangle is 13 inches long. Which of the following pairs of measurements could be the correct for the lengths of the other two sides of the triangle? (Note: A2 + B2= C2)
A.
5 inches, 12 inches
B.
2.5 inches, 6 inches
C.
2.5 inches, 4 inches
D.
5 inches, 8 inches
To determine which pair of measurements for the other two sides of the triangle is correct, we need to use the Pythagorean theorem, which states:
A2+B2=C2A^2 + B^2 = C^2A2+B2=C2
where CCC is the hypotenuse of the right triangle.
In this case, the hypotenuse CCC is 13 inches. We need to check which pair of measurements for AAA and BBB satisfies:
A2+B2=132A^2 + B^2 = 13^2A2+B2=132 A2+B2=169A^2 + B^2 = 169A2+B2=169
Let’s evaluate each option:
- A. 5 inches, 12 inches52+122=25+144=1695^2 + 12^2 = 25 + 144 = 16952+122=25+144=169This satisfies the Pythagorean theorem.
- B. 2.5 inches, 6 inches2.52+62=6.25+36=42.252.5^2 + 6^2 = 6.25 + 36 = 42.252.52+62=6.25+36=42.25This does not satisfy the Pythagorean theorem.
- C. 2.5 inches, 4 inches2.52+42=6.25+16=22.252.5^2 + 4^2 = 6.25 + 16 = 22.252.52+42=6.25+16=22.25This does not satisfy the Pythagorean theorem.
- D. 5 inches, 8 inches52+82=25+64=895^2 + 8^2 = 25 + 64 = 8952+82=25+64=89This does not satisfy the Pythagorean theorem.
Correct answer: A