A rectangular flower bed covers an area of 11.76 square feet in the garden. The width of the flower bed is 3.5 feet less it’s length

Question

Find the length and width of the flower bed

Answer 1

Greetings! Lets solve this shall we ?

So, we must find the dimensions of this rectangular flower bed given the area of 11.76 square feet and the width of 3.5 feet less than the length. This translates into w = x - 3.5, where the length is l = x. Then, we yield the area of a rectangle such that

l*w = A

(x)(x-3.5) = 11.76.........Distribute the x inside to obtain

x² - 3.5x = 11.76.......Then subtract 11.76 to the other side to obtain

x² - 3.5x - 11.76 = 0........Then we try and factor and notice we must use the Quadratic Formula such that

a = 1 , b = -3.5 and c = -11.76. Then

3.5 ± √(12.25 + 47.04) / 2 = 3.5 ± √(59.29) / 2 = (3.5 + 7.7) / 2 = x = 5.6....We only use the positive x value because the other one is negative and we cannot have a negative length. So, the length is x = 5.6 feet.

Now we can find the width such that w = 5.6 - 3.5 = 2.1 feet.

I hope this helped!