Question

The area of a triangle is 96 cm^2 and the altitude is 4 cm greater than the base.

Find the length of the base and the altitude.

(Thanks for any help!)

Answer 1

base = 12 cm , altitude = 16 cm

Explanation:

the area (A) of a triangle is calculated as

A =
`(1)/(2)` ba ( b is the base and a the altitude )

let b = base , then a = b + 4 and A = 96 , so

`(1)/(2)` b(b + 4) = 96 ( multiply both sides by 2 to clear the fraction )

b(b + 4) = 192

b² + 4b = 192 ( subtract 192 from both sides )

b² + 4b - 192 = 0 ← in standard form

(b + 16)(b - 12) = 0 ← in factored form

equate each factor to zero and solve for b

b + 16 = 0 ⇒ b = - 16

b - 12 = 0 ⇒ b = 12

however, b > 0 , then b = 12 and a = b + 4 = 12 + 4 = 16

thus base = 12 cm and altitude = 16 cm