the length of a rectangle is 3 centimeters less than twice its width. if the perimeter of the rectangle is 18 centimeters, find its dimensions.

Answer 1

Since we know that the length is 3 cm less than twice the width, we can write the length (l) in terms of width (w) as follows:

l = 2w-3

We can now move on to find the width because we are given the perimeter and we know the standard formula for the perimeter (p) of a rectangle:

p = 18 ; p = 2l+2w

Substituting 18 for p and 2w-3 for l, we can say

18 = 2(2w-3)+2w

18 = 4w-6+2w

18 = 6w-6

24 = 6w

where we get w=4.

Lastly, we can now substitute 4 for w in the length equation we got originally, l = 2w-3

l = 2(4)-3

l = 8-3

So l = 5 and w = 4. I hope that helps!

Answer 2

Let x = width

2x-3 = length

Perimeter = 2W + 2L Substitute in the values

18=2(x)+2(2x-3) Distribute to clear the parenthesis

18=2x+4x-6 Combine like terms

18=6x-6 Add 6 to both sides

18+6=6x-6+6 Simplify

24=6x Divide both sides by 6

24/6=6x/6 Simplify

x=4

2x-3=2(4)-3 = 8-3 = 5

The width of the rectangle is 4 cm. The length of the rectangle is 5 cm.