Quadratics

Question

The base of a triangular sail is 12 m shorter than its height. The area is 110m² . Find the base and height of the sail.

Answer 1

Let h  = the height, so the base is b = h - 12

 

Area = A = 1/2(bh)

 

110 = (1/2)[h(h - 12)] = (1/2)h² - 6h

 

h2 - 12h - 220 = 0, Solve using the Quadratic Formula or FOIL Method, to get x₁ = -10 and x₂ = 22

 

Choose 22, so the height is 22 and the base is b = 22 - 12 = 10 m

 

b = 10 m and h = 22 m

 

Check 110 = (1/2)(10)(22) = (1/2)220 = 110 m²