Question

the given lengths are two sides of a right triangle. all three side lengths of the triangle are integers, and together they form a pythagorean triple. find the length of the third side, then indicate whether it is a leg or a hypotenuse.
75, 85
a. 40, leg
b. 78, leg
c. 81, leg
d. 113, hypotenuse

please select the best answer from the choices provided

a
b
c

Explanation:

Step1: Check if 85 is hypotenuse

Let the unknown leg be $x$. Use Pythagorean theorem: $x^2 + 75^2 = 85^2$

Step2: Calculate squares

$75^2=5625$, $85^2=7225$

Step3: Solve for $x^2$

$x^2=7225-5625=1600$

Step4: Find $x$

$x=\sqrt{1600}=40$

Step5: Verify no other valid case

If 85 were a leg, hypotenuse $h=\sqrt{75^2+85^2}=\sqrt{12850}$, not integer. So 40 is the leg.

Answer:

A. 40, leg