# algebra

The base of a triangle is 8 cm greater than the height. The area is 64 cm^2. Find the height and the length of the base.

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1. height = X-cm,
Base = (X + 8)cm,

A = bh/2 = (X + 8)X/2 = 64,
Multiply both sides by 2:
(X + 8)X = 128,
X^2 + 8X = 128,
X^2 + 8X - 128 = 0,
(X - 8)(X + 16) = 0,

X - 8 = 0,
X = 8.

X + 16 = 0,
X = -16.

Use the + value of X:
X = 8cm = height.
X + 8 = 8 + 8 = 16cm = base.

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