Question

8. The length of a side and the corresponding height

Answer 1

Answer:

x = 5

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = $\frac{1}{2}$ bh ( b is the base and h the height )

Here b = x + 3 and h = 2x - 5 , thus

$\frac{1}{2}$ (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