Question

A triangle with an area of 240 square inches has a height that is 4 less than 8 times its base. Find the base and height, in inches, of the triangle.

Answer 1

base = 8 inches , height = 60 inches

Explanation:

let the base be b , then height = 8b - 4

the area (A) of a triangle is calculated as

A =
`(1)/(2)` × base × height

given A = 240, base = b and height = 8b - 4

substitute these values into the formula for A

240 =
`(1)/(2)` b (8b - 4) ← distribute parenthesis

240 = 4b² - 2b ( divide through by 2

120 = 2b² - b ( subtract 120 from both sides )

0 = 2b² - b - 120 ← quadratic equation in standard form

0 = (b - 8)(2b + 15) ← in factored form

equate each factor to zero and solve for b

b - 8 = 0 ⇒ b = 8

2b + 15 = 0 ⇒ 2b = - 15 ⇒ b = - 7.5

however, b > 0 , then b = 8

and height = 8b - 4 = 8(8) - 4 = 64 - 4 = 60

the base of the triangle is 8 inches and the height is 60 inches