Question

A rectangular lawn measuring 9m by 4m is surrounded by a flower bed with uniform width. The combined area of the lawn and the flower bed is 165 m². What is the width of the flower bed? Please write all the steps.

a) 2.5m

b) 3m

c) 3.5m

d) 4m

Answer 1

To find the width of the flower bed, we need to calculate the area of the lawn and set up an equation with the combined area. Solving the equation will give us the width of the flower bed. The width of the flower bed is approximately 7.75 meters.

Step-by-step explanation:

To find the width of the flower bed, we need to first determine the combined area of the lawn and the flower bed. We know that the area of a rectangle is given by the formula length × width. So, the area of the lawn can be calculated as 9m × 4m = 36m². Let's assume the width of the flower bed as x meters. Since the flower bed surrounds the lawn on all sides, the length and width of the combined lawn and flower bed will be increased by twice the width of the flower bed.

So, the length of the combined lawn and flower bed will be 9m + 2x meters, and the width will be 4m + 2x meters. The area of the combined lawn and flower bed can be calculated as (9 + 2x) meters × (4 + 2x) meters = 165m².

Expanding and rearranging the equation, we get 36 + 18x + 8x + 4x² = 165. Simplifying this equation, we have 4x² + 26x - 129 = 0. Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. The solutions are x = -3.25 and x = 7.75. Since we are dealing with measurements, a negative value doesn't make sense. Therefore, the width of the flower bed is approximately 7.75 meters.