Question

A graphics designer is designing an advertising brochure for an art show. Each page of the brochure is rectangular with an area of 52 in^2 and a perimeter of 30in. Find the dimensions of the brochure. The longer side is _____in. The shorter side is ______ in.

Answer 1

9514 1404 393

Answer:

• 9.562 in
• 5.438 in

Explanation:

The sum of side lengths of a rectangle is half the perimeter, so is 15 inches for this brochure. If x is one of the side lengths, then (15 -x) is the other one, and the area is ...

x(15 -x) = 52

x^2 -15x = -52 . . . . multiply by -1 and expand

(x -7.5)^2 = -52 +56.25 = 4.25 . . . complete the square

x = 7.5 ±√4.25 ≈ {5.438, 9.562} . . . inches

The longer side is 7+√4.25 ≈ 9.562 inches; the shorter side is 7-√4.25 ≈ 5.438 inches.