Question

A triangle has a height that is 2 inches taller than its base and an area of 12 square inches. What are the dimensions of the triangle.

Answer 1

Let the length of the base of a triangle is x inches then the length of its height is

(x+2) inches, accordingly:

Area of the A = x.(x+2)/2 = 12.

or, x^2 + 2.x = 24. or, x^2. + 2.x - 24 = 0.

or, (x+6).(x-4) = 0.

or, x = -6 (not valid), 4.

Thus, base = 4 inches., height = (x+2) = (4+2) = 6 inches. and hypotenuse

=√{4^2+6^2)=√ 52. = 2√13 inches. Answer.