The length of a rectangular garden is 4 ft less than 3 times its width?

Question

If the perimeter of the garden is 32 ft, find the dimensions of the garden

Answer 1

Make two simultaneous equations and solve them.

L = 3W - 4
Perimeter = 2(L+W) = 32

plug L into the second equation and solve it for W. Once you have W, plug it into the first equation to get L.

Answer 2

Let's make the sides lengths L and W

.......... L
______________
|........................|
|........................| W
|______________|


That means
2L + 2W = 32 (add all 4 sides together to get the perimeter)

Now, the problem tells us that L + 4 = 3W (We have to add 4 to the length to equal 3 times the width.)

So, solving for L: L + 4 - 4 = 3W -4
L = 3W - 4

Now, plugging into the 1st equation:

2L + 2W = 32
2(3w - 4) + 2w = 32
6w - 8 +2w = 32
8w - 8 +8 = 32 +8
8w = 40
w = 5

That means that if L = 3W - 4, then L = 3(5) - 4 = 11

W = 5, L = 11

Try checking it. Perimeter = 5 + 5 +11 +11 = 32.

Yep, it's right.

Answer 3

L = length
W = width
P = perimeter = 32 ft

L is 4ft less than 3 times its W means:
L = 3W - 4
because the Perimeter is equal to 2W + 2L,
we can write it as
P = 2W + 2(3W - 4) ---> substituting L with 3W - 4
then
32 = 2W + 6W - 8
32 = 8W - 8
40 = 8W

W = 5 ft
L = 3W - 4 = 3(5) - 4 = 11 ft

Answer 4

L + 4 = 3w
2L +2w = 32
2L - 6w = -8
8w = 40

w = 5
L = 11