# The length of a rectangular garden is 2 feet longer than 3 times its width. If the perimeter of the garden is 100 feet find the width and the length of the garden

hala718 | Certified Educator

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Let the length of the rectangle be L, and the width be W.

Given that the length is 2 ft longer than 3 times w.

Then we write: L = 2 + 3w...........(1)

Also, given that the perimeter is 100 ft.

==> P = 2L + 2W = 100

We will divide by 2.

==> L + W = 50 ........(2).

Now we will solve the system by substitution.

==> 2+3W + W = 50

==> 2 + 4W = 50

==> Subtract 2 from both sides.

==> 4W = 48

Now divide by 4.

==> W = 48/4 = 12

==> L = 2+ 3w = 2+ 3*12 = 2+36 = 38

Then the width is 12 ft and the length is 38 ft.

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## Related Questions

justaguide | Certified Educator

calendarEducator since 2010

starTop subjects are Math, Science, and Business

The length of a rectangular garden is 2 feet longer than 3 times its width. The perimeter of the garden is 100 feet.

We have to find the width and the length of the garden.

The perimeter of a rectangle with length L and width W is given by 2*(L + W)

Here length = 2 + 3* width

=> L = 2 + 3W

The perimeter = 2L + 2W = 100

=> 2(2 + 3W) + 2W = 100

=> 4 + 6W + 2W = 100

=> 8W = 96

=> W = 12

L = 2 + 3*12 = 2 + 36 = 38

The length of the garden is 38 feet and the width is 12 feet.

check Approved by eNotes Editorial