Question

A billboard is a = 14 feet longer than it is high (see figure). The billboard has 792 square feet of advertising space. What are the dimensions of the billboard?

Length: _____ft

Height: ______ ft

Dimensions (USING THE FIGURE) of the billboard: Length: h+a

Height: h

Answer 1

Let the height of the billboard be x ft. Then its length is x +14 ft. so that its area is length* height = (x+14) x = x²+14x. Thus, x²+14x = 792 or, x²+14x-792 = 0. Now, on using the quadratic formula, we get x = [-14±√{ 14² -4*1*(-792)} /2*1 = [-14±√(196+3168)]/2 = (-14±√3364)/2   = (-14±58)/2. Since x cannot be negative, we have x = (-14+58)/2 = 44/2 = 22. Thus, the length of the billboard is 22+14 = 36 ft. and its height is 22 ft.

  Length: 36 ft.

Height: 22 ft.