Question

A garden measuring 12m by 16m is to have a pedestrian pathway that is w meters wide installed all the way around so that it increases the total area to 285 m². What is the width of the pathway?​

Answer 1

The width of the pathway can be found by setting up and solving the equation (12+2w)(16+2w) = 285, using the formula for area of a rectangle and the given areas of the garden before and after installation of the pathway.

Step-by-step explanation:

To solve this problem, we first need to remember the formula for the area of a rectangle, which is length x width. The original area of the garden is 12m x 16m = 192 sq m. Now, when we add the pedestrian pathway all around the garden, the length and width both increase by 2w (w on each side).

So, the new length and width are (12+2w)m and (16+2w)m respectively. The area of the garden including the path is then (12+2w)m x (16+2w)m, and we know this equals 285 sq m (given in the problem).

Setting up the equation (12+2w)(16+2w) = 285, simplifying, and solving for 'w' will give you the width of the pathway.

Learn more about Area of a Rectangle