Answer:
[tex] \huge{ \boxed{ \bold{ \sf{Length \: = \: 4 \: cm}}}}[/tex]
[tex] \huge{ \boxed{ \bold{ \sf{Width = 5 \: cm}}}}[/tex]
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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 :
[tex] \boxed{ \sf{Perimeter \: of \: a \: rectangle = 2(L + W)}}[/tex]
Plug the values and solve for L
➺ [tex] \sf{18 = 2(L+ 2L - 3)}[/tex]
➺ [tex] \sf{18 = 2(3L - 3)}[/tex] { Add : 2L and L )
➺ [tex] \sf{18 = 6L - 6}[/tex] { Distribute 2 through the parentheses )
➺ [tex] \sf{6L - 6 = 18}[/tex] { Swipe the sides of the equation }
➺ [tex] \sf{6L = 18 + 6}[/tex] { Move 6 to right hand side and change it's sign )
➺ [tex] \sf{6L = 24}[/tex] { Add the numbers : 18 and 6 }
➺ [tex] \sf{ \frac{6L}{6} = \frac{24}{6}} [/tex] { Divide both sides by 6 }
➺ [tex] \boxed{ \sf{length \: ( \: L\: ) \: = \: 4 \: cm}}[/tex]
☞ Now , Evaluating 2L - 3 when L = 4 cm in order to find the value of width of a rectangle : [tex] \sf{2l - 3}[/tex]
➺ [tex] \sf{2 \times 4 - 3}[/tex] { Plug the value of length }
➺ [tex] \sf{8 - 3}[/tex] { Multiply 2 by 4 }
➺ [tex] \boxed{ \sf{Width \: ( \: W \: ) \: = \: 5 \: cm}}[/tex]
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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