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The perimeter of a rectangle is 38”. If the length is 3” morb than the width, find the width

The perimeter of a rectangle is 38”. If the length is 3” morb than the width, find-example-1
User PravinDodia
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1 Answer

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10 votes

To answer this question we will use the following formula for the perimeter of a rectangle:


Perimeter=2(length+width).

Since the perimeter of the rectangle is 38'' and the length is 3''' more than the width, then we can set the following system of equations:


\begin{gathered} 38^(\prime)^^(\prime)=2(length+width), \\ length=width+3^(\prime)^(\prime)^(\prime). \end{gathered}

Substituting the second equation in the first one we get:


38^(\prime\prime)=2(width+3^(\prime)^(\prime)^(\prime)+width).

Simplifying the above result we get:


\begin{gathered} 38^(\prime)^(\prime)=2(2width+3^(\prime)^(\prime)^(\prime)) \\ =4width+6^(\prime\prime\prime). \end{gathered}

We know that:


1^(\prime)^(\prime)^(\prime)=(1)/(12)^(\prime)^(\prime).

Therefore:


38^(\prime)^(\prime)^=4width+(1)/(2)^(\prime)^(\prime).

Subtracting 1/2'' from the above result we get:


\begin{gathered} 38^(\prime)^(\prime)-(1)/(2)^(\prime)^(\prime)=4width+(1)/(2)^(\prime)^(\prime)-(1)/(2)^(\prime)^(\prime), \\ 37(1)/(2)^(\prime)^(\prime)=4width. \end{gathered}

Dividing the above result by 4 we get:


9(3)/(8)^(\prime)^(\prime)=width.

User Osg
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