The hypotenuse (side C) of a triangle is 13 inches long. Which of the following pairs of measurements could be correct for the lengths of the other two sides of the triangle? (Note: N + 82 =C2)

A. 2.5 inches,4 inches

B. 2.5 inches, 6 inches

C.5inches, 8inches

D.5inches, 12inches

Thank you!

5 inches, 12 inches

D. 5 inches, 12 inches

5-12-13

Pls how do you find sides of an angle with a given hypotenuse & unknown sides?

a^2 + b^2 = c^2

5^2 + 12^2= 13^2
25+144=169
169=169
5-12-13

To solve this problem, we can use the Pythagorean theorem. According to the Pythagorean theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, let's assume that side A and side B are the other two sides.

The Pythagorean theorem can be written as:
A^2 + B^2 = C^2

Given that the hypotenuse (C) is 13 inches long, we can substitute this value into the equation:
A^2 + B^2 = 13^2

Solving for each answer option:

A. 2.5 inches, 4 inches:
(2.5)^2 + (4)^2 = 6.25 + 16 = 22.25
22.25 does not equal 13^2, so this pair of measurements is incorrect.

B. 2.5 inches, 6 inches:
(2.5)^2 + (6)^2 = 6.25 + 36 = 42.25
42.25 does not equal 13^2, so this pair of measurements is incorrect.

C. 5 inches, 8 inches:
(5)^2 + (8)^2 = 25 + 64 = 89
89 does not equal 13^2, so this pair of measurements is also incorrect.

D. 5 inches, 12 inches:
(5)^2 + (12)^2 = 25 + 144 = 169
169 equals 13^2, so this pair of measurements is correct.

Therefore, the correct pair of measurements for the lengths of the other two sides of the triangle is 5 inches and 12 inches, which is option D.

There are several standard right triangles with integer sides. It will help a lot if you just learn them -- they turn up often in problems, and it's nice not to have to do the calculations every time.

3-4-5
5-12-13
8-15-17
7-24-25

and multiples of those values