Answer:
height = 12 m
Step-by-step 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 = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height ), thus
A = [tex]\frac{1}{2}[/tex] x(2x + 6)
Given A = 18, then
[tex]\frac{1}{2}[/tex] 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
