Question

a triangular sign has a base that is to be 4 feet less than twice its height. A local zoning ordinance restricts the area of the signs to be equal 24 square feet. find the base and height diminsions

Answer 1

The base is 8 ft and the height is 6 ft.

Explanation:

If the height of the triangle is x feet its base = 2x - 4 feet.

So the area of the triangle

= 1/2 * base * height

= 1/2 * (2x - 4) * x = 24

(x - 2) * x = 24

x^2 - 2x - 24 = 0

(x - 6)(x + 4) = 0

x = 6, -4 As x is the height it must be 6 feet.

The base = 2x - 4 = 2(6) - 4 = 8 feet.