Question

The width of a rectangle is 3 cm less than twice its length. If the perimeter of the

rectangle is 18 cm, find its dimensions.

Answer 1

`\huge{ \boxed{ \bold{ \sf{Length \: = \: 4 \: cm}}}}`

`\huge{ \boxed{ \bold{ \sf{Width = 5 \: cm}}}}`

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☯ Question :

• The width of a rectangle is 3 cm less than twice its length. If the perimeter of the rectangle is 18 cm, find its dimensions.

☯ Step - by - step explanation :

✒ First, Let length of a rectangle be ' L '.

✑ Given :

• Width of a rectangle = 3 cm less than twice its length ( i.e W = 2L - 3 )
• Perimeter of a rectangle ( P ) = 18 cm

☞ Finding value of length of a rectangle :

`\boxed{ \sf{Perimeter \: of \: a \: rectangle = 2(L + W)}}`

Plug the values and solve for L

➺
`\sf{18 = 2(L+ 2L - 3)}`

➺
`\sf{18 = 2(3L - 3)}` { Add : 2L and L )

➺
`\sf{18 = 6L - 6}` { Distribute 2 through the parentheses )

➺
`\sf{6L - 6 = 18}` { Swipe the sides of the equation }

➺
`\sf{6L = 18 + 6}` { Move 6 to right hand side and change it's sign )

➺
`\sf{6L = 24}` { Add the numbers : 18 and 6 }

➺
`\sf{ (6L)/(6) = (24)/(6)}` { Divide both sides by 6 }

➺
`\boxed{ \sf{length \: ( \: L\: ) \: = \: 4 \: cm}}`

☞ Now , Evaluating 2L - 3 when L = 4 cm in order to find the value of width of a rectangle :
`\sf{2l - 3}`

➺
`\sf{2 * 4 - 3}` { Plug the value of length }

➺
`\sf{8 - 3}` { Multiply 2 by 4 }

➺
`\boxed{ \sf{Width \: ( \: W \: ) \: = \: 5 \: cm}}`

Hence ,

• Length of a rectangle ( L ) = 4 cm
• Width of a rectangle ( W ) = 5 cm

Hope I helped!

Have a wonderful day! ツ

~TheAnimeGirl ♡

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Answer 2

length=4

Width=2×4-3=5

Explanation:

Let length =X

Width =2x-3

Perimeter=18

2(length+width)=18

2(X+2x-3)=18

3x-3=9

3x=12

X=12/3

X=4

So length=4

Width=2×4-3=5