Question

a rectangular garden is 30 ft by 40 ft. Part of the garden is removed in order to install a walkway of uniform width around it. The area of the new garden is one-half the area of the old garden. How wide is the walkway

Answer 1

Answer:

The wide of the walkway is 5ft.

Step-by-step explanation:

In first place you have a rectangular garden of 30ft by 40 ft  as shown in Figure 1 (Added file).

So, the area of this rectangle is:

$Area of rectangle = width * length = 30ft * 40ft =1200ft$

Area=1200ft

Now, the new garden has a walkway of uniform width around it, and the area of the new rectangle is one-half the area of the old garden

$Area of the new garden= \frac{1200}{2} =600ft$

In order to be a walkway of uniform width it's necessary to substract of each side the same amount, for this case will be 5 ft, as shown in the Figure 2. Now the new rectangule is 20ft by 30ft.

$Areaofthenewrectangle=20ft*30ft=600ft$

Which is exactly one-half the area of the old garden.

This means the width of the walkway is 5ft.