Question

The height of a triangle is 4 feet less than the length of its base, b. The area of the triangle is 30 square feet.

Find the base and the height of the triangle.

Answer 1

b = 10 ft , h = 6 ft

Explanation:

the area (A) of a triangle is calculated as

A =
`(1)/(2)` bh ( b is the base and h the height )

let base = b theh height h = b - 4

given A = 30 , then

`(1)/(2)` b(b - 4) = 30 ( multiply both sides by 2 to clear the fraction )

b(b - 4) = 60 ← distribute parenthesis on left side by b

b² - 4b = 60 ( subtract 60 from both sides )

b² - 4b - 60 = 0

(b - 10)(b + 6) = 0

equate each factor to zero and solve for b

b - 10 = 0 ⇒ b = 10

b + 6 = 0 ⇒ b = - 6

however, b > 0 , then b = 10

and h = b - 4 = 10 - 4 = 6

then base is 10 ft and height is 6 ft