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 =
`(1)/(2) b h`

let h = x
thus b = x + 2

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

⇒
`24 = (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)