Answer:
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
