Answer:
x = 5
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = x + 3 and h = 2x - 5 , thus
[tex]\frac{1}{2}[/tex] (x + 3)(2x - 5) = 20 ( multiply both sides by 2 )
(x + 3)(2x - 5) = 40 ← expand factors on left 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 , hence x = 5
