**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)**

5 inches, 12 inches

2.5 inches, 6 inches

2.5 inches, 4 inches

5 inches, 8 inches

*Correct Answer : A*

In this problem, we take the triangle as a right-angled triangle and label it as follows:

From the Pythagoras theorem A2 + B2= C2, we can look for a combination of A and B that when the squares of A and B are summed give a square of 13. Mathematically,

But C=13 inches

If we take A=5 inches and B=12 inches, then

Next, we take A=2.5 inches, B=6 inches

Next, we take A=2.5 inches, B=4 inches

*6.25+16=169*

*22.25≠169*

Taking A=5 inches and B=8 inches

From the above computation, the combination of A=5 inches and B=12 inches give a triangle with a hypothenuse of 13 inches.

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