Question

The length of the base and the height of a triangle are numerically equal. Their sum is 16 less than the number of units in the area of the triangle. Find the area of the triangle.

Answer 1

let the height be x
then the base is x

area of triangle = (1/2)x^2
sum = 2x

2x = (1/2)x^2 - 16
4x = x^2 - 32
x^2 - 4x - 32 = 0
(x-8)(x+4) = 0
x = 8 or x = -4, the latter makes no sense,

so if x=8, area = (1/2)64 = 32

check
is their sum 16 less than the area?
or
is 16 less than 32 by 16 ? , YES