+110 A right triangle has legs of length 6 and x, and a hypotenuse of length y. The perimeter of the triangle is 18. Compute y.
+129850 We have that
6 + x + y = 18
And we know that y = sqrt [ 6^2 + x^2]
So we have that
6 + x + sqrt [ 6^2 + x^2] = 18 simplify
x + sqrt [ 6^2 + x^2 ] = 12
sqrt [ 6^2 + x^2] = 12 - x square both sides
6^2 + x^2 = x^2 - 24x + 144 rearrange as
24x - 144 + 6^2 = 0
24x - 144 + 36 = 0
24x - 108 = 0
24x = 108
x = 108/24 = 9/2 = 4.5
So
y = sqrt [6^2 + 4.5^2 ] = sqrt [ 36 + 20,25 ] = sqrt [56.25 ] = 7.5
CORRECTED ANSWER!!!
