Question

The base of a triangle is 3 more than 2 times of height. Determine the dimensions that give total area of 10 square feet.

Answer 1

height = 2.5 ft , base = 8 ft

Explanation:

the area (A) of a triangle is calculated as

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

height = h then base = 2h + 3 and A = 10 , then

`(1)/(2)` h(h + 3) = 10 ( multiply both sides by 2 to clear the fraction )

h(h + 3) = 20 , that is

h² + 3h = 20 ( subtract 20 from both sides )

h² + 3h - 20 = 0 ← in standard form

(h + 4)(2h - 5) = 0 ← in factored form

equate each factor to zero and solve for h

h + 4 = 0 ⇒ h = - 4

2h - 5 = 0 ⇒ 2h = 5 ⇒ h = 2.5

but h > 0 , then h = 2.5

and 2h + 3 = 2(2.5) + 3 = 5 + 3 = 8

that is height = 2.5 ft and base = 8 ft