The value for n using quadratics

n = 10

Step-by-step explanation:

Given width = n + 6 and height is 13 less than width, then

height = n + 6 - 13 = n - 7

The area (A) of a triangle is calculated as

A = wh ( w is the width and h the height )

Here A = 24, w = n + 6 and h = n - 7 , thus

(n + 6)n - 7) = 24 ( multiply both sides by 2 )

(n + 6)(n - 7) = 48 ← expand left side using FOIL

n² - n - 42 = 48 ( subtract 48 from both sides )

n² - n - 90 = 0 ← in standard form

(n - 10)(n + 9) = 0 ← in factored form

Equate each factor to zero and solve for n

n - 10 = 0 ⇒ n = 10

n + 9 = 0 ⇒ n = - 9

However, n > 0, thus n = 10