Question

The area of a triangle is 24 square meters. The base is 2 meters more than the height. What are the base, b, and the height, h, of the triangle

Answer 1

A of Δ = $\frac{1}{2} b h$

let h = x
thus b = x + 2

If A = 24 
  by substituting b, h and A into equation

⇒  $24 = \frac{1}{2} ( x + 2)(x)$

⇒  $24 * 2 = x^{2} + 2x$

⇒  $x^{2} + 2x - 48 = 0$

⇒ x² + 8x - 6x - 48 = 0

⇒ (x + 8) (x - 6) = 0

   thus x = -8  OR  x = 6 

∴ height = 6 m; base = 8 m  ( x = -8  was disregarded since a                                                                       measurement of this kind cannot be negative)