Each end of a glass prism is a triangle with a height that is 1 inch shorter than twice the base. If the area of the triangle is 60 square inches, how long are the base and height?

Step-by-step explanation:

Let the base = x inches

So, h = 2x - 1

Area of triangle = 60 square inches

(1/2) * base * height = 60

(1/2) * x * (2x-1) = 60

x * (2x-1) = 60*2

2x² - x = 120

2x² - x - 120 = 0

2x² - 16x + 15x - 15*8 = 0

2x (x - 8) + 15 (x - 8) = 0

(x-8) (2x + 15) = 0

x - 8 = 0 {ignore 2x + 1 as it will give negative value}

x = 8

Base = 8 inches

Height = 2*8 - 1 16 - 1 = 15 inches