Perimeter of a Rectangle

Question

The perimeter of a rectangle is 80 feet.  Find the dimensions if the length is 5 feet longer than 4 times the width.  Then find the area of the rectangle.

 

I know that P=2(l+w)

Answer 1

l = 4w + 5

P = 2[(4w + 5) + w] = 80

(4w + 5) + w = 80 / 2

5w + 5 = 40

5w = 40 - 5

w = 35 / 5 = 7 feet

l = 4 * 7 + 5 = 33 feet

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Verify the answer:

2(33 + 7) = 80
2 * 40 = 80
   80 = 80

Answer 2

Hi Conny;

L=4W+5

80=2L+2W

80=2(4W+5)+2W

80=8W+10+2W

Let's combine like terms...

80=10W+10

Let's subtract 10 from both sides as we proceed to isolate x...

80-10=10W+10-10

70=10W

Let's divide both sides by 10...

70/10=(10W)/10

7=W

L=4W+5

L=4(7)+5

L=28+5

L=33

 

Let's check our work...

2W+2L=80

[2(7)]+[2(33)]=80

14+66=80

80=80