Question

A rectangular garden is 40 ft longer than it is wide. Its area is 3,200 ft². What are its dimensions (in ft)?

a) 40 ft x 80 ft

b) 60 ft x 100 ft

c) 50 ft x 90 ft

d) 70 ft x 110 ft

Answer 1

The correct answer is A. To find the dimensions of the rectangular garden, set up an equation using the width and length, and solve for the width using quadratic equations. The possible dimensions of the garden are 40 ft by 80 ft.

Step-by-step explanation:

To solve this problem, let's assume that the width of the rectangular garden is x ft. Since the garden is 40 ft longer than it is wide, the length is x + 40 ft. The area of a rectangle is found by multiplying the length by the width, so we can set up the equation: x(x + 40) = 3200.

Expanding and rearranging the equation, we get: x^2 + 40x - 3200 = 0. This is a quadratic equation that can be solved by factoring or using the quadratic formula.

After solving the equation, we find that the possible dimensions of the garden are 40 ft x 80 ft.