### Home > CC3 > Chapter 9 > Lesson 9.2.2 > Problem9-75

9-75.

Lydia has four straws of different lengths, and she is trying to form a right triangle.  The lengths are $8, 9, 15,$ and $17$ units.  Which three lengths should she use?  Justify your answer.

The Pythagorean Theorem states that for any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.$\text{(leg 1)}^2 + \text{(leg 2)}^2 = \text{(hypotenuse)}^2$

Square every length.

$(8)^2 = 64$
$(9)^2 = 81$
$(15)^2 = 225$
$(17)^2 = 289$

The lengths cannot be $8, 9,$ and $15$ because: $(8)^2 + (9)^2 ≠ (15)^2$.
Find the right combination of lengths that make the equation true.