Question

The perimeter of a rectangle is 168 m. Its length is five times its width. Find the length and width.

Answer 1

Answer:

• Length = 70 metre

• Width = 14 metre

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Step-by-step explanation :

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As, it is given that, the perimeter of a rectangle is 168 m and its length is five times its width and we are to find the length and width of the rectangle. So,

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Let us assume the width of the rectangle as w metre and therefore, the length will be 5w metre .

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Now, According to the Question :

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`{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_((Rectangle)) }}}}`

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`{\longrightarrow \qquad { {\sf{2 (5 w + w )= 168 }}}}`

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`{\longrightarrow \qquad { {\sf{2 (6 w )= 168 }}}}`

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`{\longrightarrow \qquad { {\sf{12 w = 168 }}}}`

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`{\longrightarrow \qquad { {\sf \: w = (168)/(12) }}}`

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`{\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ w = 14 }}}}}} \: \: \bigstar`

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Therefore,

• The width of the rectangle 14 metre .

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Now, we are to find the length of the rectangle :

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`{\longrightarrow \qquad { { { \pmb {\frak{ Length = 5w }}}}}} \: \:`

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`{\longrightarrow \qquad { { { \pmb {\frak{ Length = 5 * 14 }}}}}} \: \:`

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`{\longrightarrow \qquad { \underline{ \boxed{ \pmb {\frak{ Length = 70 }}}}}} \: \: \bigstar`

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Therefore,

• The length of the rectangle is 70 metre

Answer 2

• Length of rectangle = 63 m
• Width of rectangle = 21 m

Explanation:

Given:

• Perimeter of rectangle = 168 m
• Length of rectangle is five times the width

To Find:

• Length and Width

Solution:

Let's assume width of rectangle x m and length of rectangle be 3x m. To calculate the dimensions of the rectangle we will use the formula of Perimeter of the rectangle

Perimeter of rectangle = 2(L + B)

Substituting the required values:

→ 168 = 2(3x + x)

→ 168 = 2(4x)

→ 168/2 = 4x

→ 84 = 4x

→ 84/4 = x

→ 21 = x

Hence,

• Length of the Rectangle = 3x = 3(21) = 63 m
• Wdith of the rectangle = x = 21 m