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#