The area of a triangular flag is 72 square centimeters.

Question

The area of a triangular flag is 72 square centimeters. Its altitude is 2 centimeters longer than twice its base. Find the lengths of the altitude and the base.

Answer 1

Let x = length of the base

 

Then, 2x + 2 = length of the altitude

 

Area of triangle = ½(base)(altitude)

 

So, ½(x)(2x + 2) = 72

 

Simplify to get x² + x - 72 = 0

 

(x + 9)(x - 8) = 0

 

x = -9 or x = 8

 

Since x can't be negative, x = 8

 

base      = x = 8 cm

altitude = 2x + 2 = 18 cm