Application problem

Question

The height of a triangle is 5in less than the length of the base. The triangle is 42in² find the base and the height of the triangle.

Answer 1

let x = base

let x-5 = height

Area of a tringle = 1/2 base x height

42 = 1/2 (x)(x-5)

Multiple both sides by 2 to clear the clear the fraction

(2)42 = (2)1/2 (x)(x-5)

Simplify

84 = x(x-5)

Distributive property

84=x²-5x

Subtract 84 from both sides of the equation

84-84=x²-5x-84

Simplify

0=x²-5x-84

Can solve this by factoring

0=(x+7)(x-12)

Set both factors equal to zero and solve.

x+7=0 and x-12=0

x=-7 and x=12 -7 cannot be a dimension for a triangle, so the only valid solution is x=12

let x = base = 12 in

let x-5 = height = 7 in