half the perimeter of a rectangle garden whose length is 4cm more than its width 36cm find the dimensions of garden
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half the perimeter of a rectangle garden whose length is 4cm more than its width 36cm find the dimensions of garden
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Answer:
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Answer:
Given :-
To Find :-
Solution :-
Let,
[tex]\mapsto \bf Width_{(Rectangular\: Garden)} =\: x\: cm\\[/tex]
[tex]\mapsto \bf Length_{(Rectangular\: Garden)} =\: (x + 4)\: cm\\[/tex]
Given :
According to the question by using the formula we get,
[tex]\small \implies \sf\boxed{\bold{Perimeter_{(Rectangle)} =\: 2(Length + Width)}}\\[/tex]
But the perimeter will be the half so,
[tex]\implies \sf 36 =\: \dfrac{\cancel{2}(Length + Width)}{\cancel{2}}\\[/tex]
[tex]\implies \sf 36 =\: Length + Width\\[/tex]
[tex]\implies \sf 36 =\: x + 4 + x\\[/tex]
[tex]\implies \sf 36 =\: x + x + 4\\[/tex]
[tex]\implies \sf 36 =\: 2x + 4\\[/tex]
[tex]\implies \sf 36 - 4 =\: 2x\\[/tex]
[tex]\implies \sf 32 =\: 2x\\[/tex]
[tex]\implies \sf \dfrac{32}{2} =\: x\\[/tex]
[tex]\implies \sf 16 =\: x\\[/tex]
[tex]\implies \sf\bold{x =\: 16}\\[/tex]
Hence, the required length and width of a rectangular garden will be :
[tex]\dag[/tex] Length Of Rectangular Garden :
[tex]\dashrightarrow \sf Length_{(Rectangular\: Garden)} =\: (x + 4)\: cm\\[/tex]
[tex]\dashrightarrow \sf Length_{(Rectangular\: Garden)} =\: (16 + 4)\: cm\\[/tex]
[tex]\dashrightarrow \sf\bold{\underline{Length_{(Rectangular\: Garden)} =\: 20\: cm}}\\[/tex]
[tex]\dag[/tex] Width Of Rectangular Garden :
[tex]\dashrightarrow \sf Width_{(Rectangular\: Garden)} =\: x\: cm\\[/tex]
[tex]\dashrightarrow \sf\bold{\underline{Width_{(Rectangular\: Garden)} =\: 16\: cm}}\\[/tex]
[tex]\therefore[/tex] The length of a rectangular garden is 20 cm and the width of a rectangular garden is 16 cm .