The base of a triangle is 2.1m longer than its height. If the triangles area is 9.35m, what are the base and height of the triangle in feet?

Question

The base of a triangle is 2.1m longer than its height. If the triangles area is 9.35m, what are the base and height of the triangle in feet?

Answer 1

we know that the Area of a triangle = 1/2 bh

we are given that the Area = 9.35m²

let the height =h, then the base = h + 2.1m

our formula becomes 9.35m² = 1/2 (h • (h + 2.1m))

which becomes 2 • 9.35m² = h • (h + 2.1m)

expanding, we get 18.7m² = h² + h2.1m

combining, we get h² + 2.1h - 18.7m² = 0

we can solve this equation using the quadratic formula

[-b ± √b² - 4ac] / 2a

 

we get two roots, -3.4m and +3.4m, but we will discard the negative root because a length cannot be a negative number.

 

So, the height is 3.4m, and the base is 5.5m

we then convert those numbers to feet using the conversion factor for meters to feet 1 meter  = 3.28f to get 11.15f and 18.04f

 

Proof: A = 1/2bh = 9.35m² = 1/2 (3.4m • 5.5m) = 9.35m²