Question

The area of the rectangular playground enclosure at South School is 500 square meters. The length of the playground is 5 meters longer than the width. How do you find the dimensions of the playground in meters?

Answer 1

See solution below.

Explanation:

Write an equation to solve the problem.

Area of rectangle = L(w)

Assuming that the width measures x meters, the length measures x + 5 meters.

500 = x(x + 5)

500 = `x^2` + 5x

0 = `x^2` + 5x - 500

As you may already know, a trinomial of the form `ax^2` + bx + c, a = 1, you must find 2 numbers that multiply to c and that add to b. Two numbers that multiply to -500 and add to +5 are +25 and -20

0 = (x + 25)(x - 20)
x = -25 and 20

Since a negative length is impossible, the width mesures 20 meters and the length measures 25 meters.

Practice exercises:

1. A rectangle has a perimeter of 90 meters. Find the maximum area.

2. The area of a right triangle is 120 `m^2`. The base measures half the sum of the height and one. Find the perimeter.

3. Find the area and perimeter of a right triangle the has a height that is 2 more than the double of the width and that has a hypotenuse that measures `sqrt68` meters.

Good luck!