The hypotenuse of a right triangle is 37 units long. Find the other two sides if the perimeter of the triangle is 84 units.
+658 Please don't just provide an answer without showing your work. I recommend not using brute force as a method too.
+658 Leg a = \(a\)
Leg b = \(b\)
By perimeter:
\(a + b+37=84\)
\(a+b=47\)
By Pythagorean Theorem:
\(a^2+b^2=37^2\)
Substitution:
\(a^2+(47-a)^2=37^2\)
Solving:
a^2+(47-a)^2=37^2 = {a=12, a=35}
a = 12
b = 35
or
a = 35
b = 12
