Find the height and base of the triangle.

Question

The base of a triangle is 5 cm greater than the height. The area is 33 cm². Find the height and base of the triangle.

Answer 1

h = length of height

h + 5 = length of base

 

33 = h(h + 5) / 2

66 = h(h + 5)

66 = h² + 5h

0 = h² + 5h - 66

0 = (h + 11)(h - 6)

 

{-11, 6}

 

Measurement is only positive

 

The height is 6 cm and the base is 11 cm.

 

Answer 2

Let x = height, then base = x + 5

 

Area = (1/2)(base)(height)

 

So, (1/2)(x)(x + 5) = 33

 

x² + 5x = 66

 

x² + 5x - 66 = 0

 

(x + 11)(x - 6) = 0     So, x = 6 or x = -11

 

Since x can't be negative, x = 6

 

Height = x = 6 cm,   Base  = x + 5 = 11 cm