Algebra word problem.

Question

A right triangle shaped sail has an area of 84 square meters. The base of the sail is 10 less than twice the height. Find the base and the height.

Answer 1

Answer 2

The units of base and height will be meters, but for simplicity, I'll be dropping the units throughout the problem.

Each of the first two sentences describes an equation involving base b and height h.

We know from the first sentence that 1/2*b*h = 84

From the second sentence, b = 2h -10

We can substitute the second equation into the first:

1/2*(2h -10)*h = 84

Multiplying the 1/2 times the expression in the parentheses gives us

(h-5)*h = 84

or h² - 5h - 84 = 0

We can now either factor or use the quadratic formula. Factoring gives us (h - 12)*(h + 7) = 0.

Since the height can't be negative, we have h = 12. Plugging that into b = 2h -10 gives us b = 24 - 10 = 14

Then we should check that our answer yields a sail area of 84: 1/2*14*12 = 84, so this answer is correct.