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The width of a rectangle is only 15% of its length. If the perimeter of the rectangle is 46, what is the length

1 Answer

3 votes

Answer:

20 units

Explanation:

Let the length be x. According to the question,

  • Length = x
  • Width = 15% of the length

➝ Width = 15% of the length

➝ Width = 15/100x

Width = 3/20x

We have the perimeter of the rectangle that is 46 units.


\longrightarrow \sf {Perimeter_((Rec.)) = 2(L + W) } \\


\longrightarrow \sf {46= 2\Bigg \lgroup x + (3)/(20)x \Bigg \rgroup } \\


\longrightarrow \sf {46= 2\Bigg \lgroup x + (3)/(20)x \Bigg \rgroup } \\


\longrightarrow \sf {46= 2\Bigg \lgroup (20x + 3x)/(20) \Bigg \rgroup } \\


\longrightarrow \sf {46= 2\Bigg \lgroup (23x)/(20) \Bigg \rgroup } \\


\longrightarrow \sf {(46)/(2)= (23x)/(20)} \\


\longrightarrow \sf {23= (23x)/(20)} \\


\longrightarrow \sf {23 * 20 = 23x} \\


\longrightarrow \sf {460= 23x} \\


\longrightarrow \sf {\cancel{(460)/(23)} = x} \\


\longrightarrow \underline{\boxed{ \bf {20\; units = x}}} \\

Therefore, length of the rectangle is 20 units.

User Mark Kasson
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