Question

the legnth of a rectangle is three times its width. if the length of the perimeter is 64 in, find the length and width

Answer 1

• Length and width of rectangle is 24 and 8 inches

Explanation:

Given:

• Length of rectangle is three times the width
• Perimeter of rectangle is 64 Inches

To Find:

• Length and Width

Solution:

Let's assume Width of rectangle x inches and length be 3x inches. To calculate the dimensions of The rectangle we will use the formula of Perimeter of rectangle:

Perimeter of rectangle = 2(L + B)

→ 64 = 2(3x + x)

→ 64 = 2(4x)

→ 64/2 = 4x

→ 32 = 4x

→ 32/4 = x

→ 8 = x

Hence,

• Length of the rectangle = 3x = 3(8) = 24 inches

• Width of the rectangle = x = 8 inches

Answer 2

• Length = 24 inches

• Width = 8 inches

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Step-by-step explanation :

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As it is given that, the legnth of a rectangle is three times its width and the perimeter is 64 in 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 inches and therefore, the length will be 3w inches .

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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 (3 x + x )= 64 }}}}`

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`{\longrightarrow \qquad { {\sf{2 (4x )= 64 }}}}`

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`{\longrightarrow \qquad { {\sf{8x= 64 }}}}`

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`{\longrightarrow \qquad { {\sf{ x = (64)/(8) }}}}`

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`{\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 8}} }}} }\: \: \bigstar`

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Therefore,

• The width of the rectangle is 8 inches .

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

`{\longrightarrow \qquad{ { \frak{\pmb{Length = 3x }}}}}`

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`{\longrightarrow \qquad{ { \frak{\pmb{Length = 3 * 8 }}}}}`

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`{\longrightarrow \qquad{ \underline{ \boxed{ \frak{\pmb{Length = 24}}}}}} \: \: \bigstar`

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Therefore,

• The length of the rectangle is 24 inches .

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