Question

The height of a triangle is 6 m more than twice the length of the base. The area of the triangle is 18 m. Find the height of the triangle

Answer 1

height = 12 m

Explanation:

let the base be x then height = 2x + 6 ( 6 more than twice the base )

The area (A) of a triangle is calculated as

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

A =
`(1)/(2)` x(2x + 6)

Given A = 18, then

`(1)/(2)` x(2x + 6) = 18

Multiply both sides by 2 to clear the fraction

x(2x + 6) = 36 ← distribute left side

2x² + 6x = 36 ( divide all terms by 2 )

x² + 3x = 18 ( subtract 18 from both sides )

x² + 3x - 18 = 0 ← in standard form

(x + 6)(x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x - 3 = 0 ⇒ x = 3

But x > 0 ⇒ x = 3

Thus height = 2x + 6 = 2(3) + 6 = 6 + 6 = 12