Question

One leg of a right triangle is 7 inches longer than the smaller leg and the hypotenuse is 8 inches longer than the smaller leg. Find the lengths ofl the side

of the triangle

Answer 1

smaller leg = x
longer leg = y
hypotenuse = z

y=x+7
z=x+8

due to

`{z}^(2) = {x}^(2) + {y}^(2) \\ (x + 8) ^(2) = {x}^(2) + (x + 7) ^(2) \\ {x}^(2) + 16x + 64 = {x}^(2) + {x}^(2) + 14x + 49 \\ {x}^(2) + 16x + 64 = 2 {x}^(2) + 14x + 49 \\ {x}^(2) - 2 {x}^(2) + 16x - 14x + 64 - 49 = 0 \\ - {x}^(2) + 2x + 15 = 0 \\ {x}^(2) - 2x - 15 = 0 \: \: (multiplied \: by \: - 1) \\ (x - 5)(x + 3) = 0 \\ then \: \: x = 5 \: \: or \: \: x = - 3`
but x cannot be -3
so smaller leg is 5 inches

then longer leg = 5+7 = 12 inches
and hypotenuse = 5+8 = 13 inches