Question

The length of a side and corresponding height of a triangle are (x+3) and (2x-5) given that area of triangle is 20cm^2. Find the value of x

Answer 1

x = 5

Explanation:

The area (A) of a triangle is calculated as

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

Here A = 20, b = (x + 3) and h = (2x - 5) , then

`(1)/(2)` (x + 3)(2x - 5) = 20 ← multiply both sides by 2

(x + 3)(2x - 5) = 40 ← expand left side using FOIL

2x² + x - 15 = 40 ( subtract 40 from both sides )

2x² + x - 55 = 0 ← in standard form

(x - 5)(2x + 11) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 5 = 0 ⇒ x = 5

2x + 11 = 0 ⇒ 2x = - 11 ⇒ x = - 5.5

But x > 0 , so x = 5