Question

A triangle's height is 10 feet more than its base. If the area of the triangle is 100 square feet, use factoring to find its dimensions.

Answer 1

The base length of the triangle is 10 ft. and the height of the triangle is 20ft.

Explanation:

Height = base + 10

Area = 100 square ft

Area of a triangle= (1/2) (b) (h)

100 = (1/2) (b) (b + 10)

200 = b(b) + 10b

b(b) + 10b - 200 = 0

b(b) + 20b - 10b - 200 = 0

b ( b + 20) -10(b + 20) = 0

(b-10) (b+20) =0

b = 10 (or) b = -20

Here b is the length and cannot be negative.

So, b = 10ft

h = b + 10

h = 10 + 10

h = 20 ft.

The base length of the triangle is 10 ft. and the height of the triangle is 20ft.