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The length of a rectangular floor is 4 ft. longer than its width w. The area of the floor is 525 ft^2.
a) Draw a picture of the situation.

b) Write a quadratic equation for the area in terms of w that represents the situation.

c) What are the dimensions of the floor? Explain how you found them.

Answer: The dimensions of the floor are 21 by 25.

For your drawing, you will have a rectangle with an x for the width and an x + 5 for the length.

If we multiply those together, we get the following equation for the area.
x(x + 5) = A
x^2 + 5x = A

Now, input 525 and solve for x.
x^2 + 5x = 525
x^2 + 5x - 525 = 0
x = 21 or x = -25

Only 21 makes sense for the width. Adding on 4 gives us 25 for the length.

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Louli Louli · Answer 2 · 2018-04-01T20:06:49+02:00

Assume that the width of the floor is w.
The length is 4 ft longer than the width.
This means that:
Length = 4 + w

Part (a):
The drawing of the situation is shown in the attached image

Part (b):
Area of the rectangle is calculated as follows:
area = length * width
area = (w + 4) * w
area = w² + 4w
We are given that the area is 525 ft²
This means that:
525 = w² + 4w

Part (c):
To get the dimensions of the floor, we will need to solve the quadratic equation from part b.
area = w² + 4w
525 = w² + 4w
w² + 4w - 525 = 0
(w-21)(w+25) = 0
either w-21 = 0 ............> w = 21 ft .........> accepted solution
or w+25 = 0 ............> w = -25 ...........> rejected solution as the length cannot be negative
Now, we know that:
length = w + 4
length = 21 + 4
length = 25 ft
This means that:
length of floor = 25 ft
width of floor = 21 ft

Hope this helps :)