Solve the problem.
-A 11 m by 16 m rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is $$456 \mathrm {~m} ^ { 2 } ?$$
A) 4 m
B) 5.5 mC)5mD)3 m

Question

Quizplus · Accepted Answer

The total area is the sum of the area of the garden and the area of the path. The area of the garden is 11 m * 16 m = 176 m^2. The area of the path is the difference between the total area and the area of the garden. Therefore, the area of the path is 456 m^2 - 176 m^2 = 280 m^2. The path is a rectangle with a length of 11 m + 2x and a width of 16 m + 2x, where x is the width of the path. The area of the path is (11 m + 2x) * (16 m + 2x) = 280 m^2. Expanding and simplifying, we get 176 m^2 + 56x m + 32x^2 = 280 m^2. Subtracting 176 m^2 from both sides, we get 56x m + 32x^2 = 104 m^2. Dividing both sides by 8, we get 7x m + 4x^2 = 13 m^2. Factoring, we get (4x + 1)(x - 3) = 0. Therefore, x = -1/4 or x = 3. Since the width of the path cannot be negative, the width of the path is 3 m.

Solve the Problem 456 m2?456 \mathrm {~m} ^ { 2 } ?456 m2?

Solve the Problem $456 \mathrm {~m} ^ { 2 } ?$