Question

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

Answer 1

Explanation:

According to the question,

Let the width of rectangle be x and length of rectangle be 3x

Perimeter of Rectangle :- 2(L+B) = 64 in

Putting the values we get ,

2(3x+x) = 64 in

8x = 64 in

x = 8 in

Putting the value of x ,

Width :- 8 Inch

Length :- 24 inch

Answer 2

Given:-

`\rightarrow` Length(l) of the rectangle is three times it's width(w) = 3w.

`\rightarrow` Width(w) of the rectangle = w.

`\rightarrow` Perimeter of the rectangle = 64in.

To Find:-

`\rightarrow`Length and width of the rectangle.

Solution:-

`\rightarrow` Perimeter of rectangle =
`\sf{2(l+w)}` putting the value of perimeter, l and w from the above given)

`\rightarrow` 64 =
`\sf{2(3w+w)}`

`\rightarrow` 64 =
`\sf{2(4w)}`

`\rightarrow` 64 =
`\sf{8w}`

`\rightarrow`
`\sf{(64)/(8)}`=
`\sf{w}`

`\rightarrow`
`\sf{8}`=
`\sf{w}`

Therefore, width of the rectangle = 8in.

And Length = 3(8)in. = 24in.

To check whether the answer is correct or not, we can put the value of length and width in the formula =
`\sf{2(l+w)}`

`\rightarrow`
`\sf{=\: 2(24+8)}`

`\rightarrow`
`\sf{=\: 2(32)}`

`\rightarrow`
`\sf{=\: 64in.}`

Since, the perimeter of the rectangle is same as given in the question, therefore the value of length and width are correct.

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Hope it helps you:)