A rectangular garden measuring 10 feet by 5 feet is to have a sidewalk that is x feet wide installed all the way around it, increasing the total area to 150 square feet. What is the width, x, of the sidewalk?

Width of sidewalk = 2.5 feet

Step-by-step explanation:

If a sidewalk that is x feet wide installed all the way around the rectangular garden, then the total length of the garden and the side walk would be (10 + 2x) feet while the total width of the garden and the side walk would be (5 + 2x) feet

The formula for determining the area of a rectangle is expressed as

Area = length * width

If the total area increased to 150 square feet, then

(10 + 2x) (5 + 2x) = 150

50 + 20x + 10x + 4x² = 150

4x² + 30x + 50 - 150 = 0

4x² + 30x - 100 = 0

4x² + 40x - 10x - 100 = 0

4x (x + 10) - 10 (x + 10) = 0

4x - 10 = 0 or x + 10 = 0

x = 10/4 or x = - 10

Since the width of the sidewalk cannot be negative, then

x = 10/4 = 2.5 feet