Question

The base of a triangle is ten more than twice the height. The area of the triangle is 126 square inches.

Answer 1

Answer:

base = 28 inches ad height = 9 inches

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 )

Let height = h then b = 2h + 10 = 2(h + 5) and A = 126, thus

$\frac{1}{2}$ 2(h + 5) × h = 126, that is

h(h + 5) = 126 ← distribute left side

h² + 5h = 126 ( subtract 126 from both sides )

h² + 5h - 126 = 0 ← in standard form

(h + 14)(h - 9) = 0 ← in factored form

Equate each factor to zero and solve for h

h + 14 = 0 ⇒ h = - 14

h - 9 = 0 ⇒ h = 9

However, h > 0 thus h = 9

height = 9 inches and base = (2 × 9) + 10 = 18 + 10 = 28 inches