Question

The perimeter of the rectangle is 98 inches The ratio of the length to the width is 4:3. What is the length and the width of the rectangle

Answer 1

Given :

• The Perimeter of the rectangle is 98 inches
• The ratio of the length to the width is 4:3.

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 4x inches. and the width is 3x inches.

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Now, Substituting the given values in the formula :

`\qquad \dashrightarrow{ \sf{2(4x + 3x )= 98}}`

`\qquad \dashrightarrow{ \sf{2(7x)= 98}}`

`\qquad \dashrightarrow{ \sf{14x= 98}}`

`\qquad \dashrightarrow{ \sf{x= (98)/(14 ) }}`

`\qquad \dashrightarrow{ \bf{x= 7}}`

Therefore,

`\qquad { \pmb{ \bf{ Length _((rectangle)) = 4x \: = 4(7) = 28 \: inches}}}\:`

`\qquad { \pmb{ \bf{ Width _((rectangle)) = 3x = 3(7) = 21 \: inches}}}\:`