The perimeter of a garden is 250 meters. the length is 5 meters more than 3 times the width, find the dimensions of the garden?

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Answer 1 · 2015-08-06T18:35:37

Width: 30 m
Length: 95 m

First, start by writing the formula for the perimeter of a rectangle

#P = 2 * (L + w)#, where

#L# - the length of the rectangle;
#w# - the width of the rectangle;

This will be your first equation. To get the second one, use the fact that the length of the perimeter is 5 m more than 3 times its width.

#L = 3 * w + 5#

Plug this into the first equation and solve for #w# to get

#2 * (3w + 5 + w) = 250#

#8w + 10 = 250#

#8w = 240 implies w = 240/8 = color(green)("30 m")#

This means that the length of th garden is

#L = 3 * (30) + 5 = color(green)("95 m")#

Give it a quick check to see if the solutions match

#2 * (30 + 95) = 250#

#2 * 125 = 250 " "color(green)(sqrt())#