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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

Sagot :

KimYurii

Answer:

20 units

Step-by-step 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.

[tex]\longrightarrow \sf {Perimeter_{(Rec.)} = 2(L + W) } \\ [/tex]

[tex]\longrightarrow \sf {46= 2\Bigg \lgroup x + \dfrac{3}{20}x \Bigg \rgroup } \\ [/tex]

[tex]\longrightarrow \sf {46= 2\Bigg \lgroup x + \dfrac{3}{20}x \Bigg \rgroup } \\ [/tex]

[tex]\longrightarrow \sf {46= 2\Bigg \lgroup \dfrac{20x + 3x}{20} \Bigg \rgroup } \\ [/tex]

[tex]\longrightarrow \sf {46= 2\Bigg \lgroup \dfrac{23x}{20} \Bigg \rgroup } \\ [/tex]

[tex]\longrightarrow \sf {\dfrac{46}{2}= \dfrac{23x}{20}} \\ [/tex]

[tex]\longrightarrow \sf {23= \dfrac{23x}{20}} \\ [/tex]

[tex]\longrightarrow \sf {23 \times 20 = 23x} \\ [/tex]

[tex]\longrightarrow \sf {460= 23x} \\ [/tex]

[tex]\longrightarrow \sf {\cancel{\dfrac{460}{23}} = x} \\ [/tex]

[tex]\longrightarrow \underline{\boxed{ \bf {20\; units = x}}} \\ [/tex]

Therefore, length of the rectangle is 20 units.

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