Question

The perimeter of a rectangle is 60 cm. The ratio of length to width is 3:2. Find the length and width of the rectangle.

Answer 1

Given :

• The Perimeter of the rectangle is 60 cm
• The ratio of the length to the width is 3:2.

To Find :

• The Length and width of the rectangle .

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Solution :

We know that,

`\qquad{ \bold{ \pmb{2(Length + Breadth ) = Perimeter_((rectangle))}}}`

Let's assume the length of the rectangle as 3x inches. and the width is 2x inches.

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Now, Substituting the given values in the formula :

`\qquad \dashrightarrow{ \sf{2(3x + 2x )= 60}}`

`\qquad \dashrightarrow{ \sf{2(6x)= 60}}`

`\qquad \dashrightarrow{ \sf{12x= 60}}`

`\qquad \dashrightarrow{ \sf{x= (60)/(12) }}`

`\qquad \dashrightarrow{ \bf{x= 5}}`

Therefore,

`\qquad { \pmb{ \bf{ Length _((rectangle)) = 3x \: = 3(5) = 15 \: inches}}}\:`

`\qquad { \pmb{ \bf{ Width _((rectangle)) = 2x = 2(5) = 10 \: inches}}}\:`