What are the dimensions of a rectangle which has a perimeter of 48 cm, if its length is 12 cm longer than twice its width?

3 Answers
Jan 9, 2018

Width: 4cm

Length: 20cm

Explanation:

Recall that the perimeter of a rectangle is twice the sum of its length and width

So we have

P=2l+2w

We are also given that the length of the rectangle in question is 12cm longer than twice it width

Then

l=12+2w

Then we can plug in

P=2w+2l=2w+2(12+2w)

And simplify

P=2w+24+4w=24+6w

Since we know that the perimeter is 48 cm we can say

P=48=24+6w

<=> subtract 24 from both sides

24=6w

<=> divide both sides by 6

4=w

Then we can plug that in to find l

l=12+2w=12+2(4)=12+8=20

Jan 9, 2018

Width = 4 cm
Length = 20 cm

Explanation:

Set:
x = width
y = length

Translate words into equations:
Equation 1: "length" = 2xx"width" + 12 " " → y = 2x + 12
Equation 2:" perimeter" = 2xx"width" + 2xx"length " → 48 = 2x + 2y

Insert equation 1 into equation 2
48 = 2x + 2y
48 = 2x + 2(2x + 12)
48 = 2x + 4x +24
24 = 6x
x = 4 cm

Find y through equation 1
y = 2x + 12
y = 2xx4 + 12
y = 20 cm

Jan 9, 2018

The width is 4 cm and the length is 20cm

Explanation:

We are told how the length of the rectangle is related to the width, so we can use one variable to define both sides.

Let the width be x

The the length is 2x+12" "larr'12 more than twice the width'

The perimeter is the sum of two widths and two lengths.

2(x) + 2(2x+12) = 48" "larr write an equation

2x+4x+24=48

6x=48-24

6x = 24

x=4

The width is 4 cm and the length is 20cm