Find the height of the triangle

Question

The height of a triangle is 2 yards less than the base. The area of of the triangle is 264 square yards. Find the height of the triangle.

Answer 1

The area of triangle = 1/2bh

Let base, b = x

h = x-2

Here given 1/2bh = 264 yards

⇒1/2(x)(x-2) = 264

 x^2-2x/2 = 264

x^2-2x =264(2)

x^2-2x =528

Apply addition property, add 1 to each side.

x^2-2x+1 = 528+1                                                        (x-1)^2 = x2+1-2x )

(x-1)^2  = 529                                                               (a-b)^2 = a^2+b^2-2ab

(x-1) =√ 529

x-1 = 23

x = 23+1

x = 24

Base = 24 yards

Height  of triangle = 24-2 = 22 yards