Question

A store is to be built on a rectangular lot that measures 60 m by 40 m. A lawn of uniform width, equal to the area of the store, must surround it.

a. How wide is the strip of lawn?
b) What are the length and width of the store?

Answer 1

To find the strip of lawn and the dimensions of the store, we set up an equation involving the total area of the lot and the area covered by the store, solving for the uniform width of the lawn.

Step-by-step explanation:

The question concerns a rectangular lot on which a store is to be built, surrounded by a uniform lawn that has an equal area to that of the store. Given that the dimensions of the lot are 60 m by 40 m, we want to find the width of the lawn strip and the dimensions of the store itself.

To solve this, let’s let x represent the width of the lawn. The area of the lot is 60 m × 40 m = 2400 m2. The area of the store will then be expressed as (60 m - 2x) × (40 m - 2x). Since the area of the store equals the area of the lawn, we set up the equation:

(60 m - 2x) × (40 m - 2x) = 2400 m2 / 2

Solving this equation will give us the value of x, the width of the lawn, and also the dimensions of the store after substituting x back into 60 m - 2x and 40 m - 2x.