The perimeter of a rectangle is 36 feet. The length is 4 feet more than the width. Calculate the length and width of the rectangle.

Answer 1

Well, we know that the perimeter is as follows:

For length L, and width W, Perimeter = L + L + W + W, or Perimeter = 2 * L + 2 * W

We are given that L = W + 4, and that Perimeter = 36 feet.

So, we just need to plug in what we know. First, let's plug the total perimeter into the equation for calculating the perimeter. So we get

Perimeter = 2 * L + 2 * W

36 = 2 * L + 2 * W

Now, let's plug in the other information we know, namely that L = W + 4. Then we can solve for W.

36 = 2 * L + 2 * W

36 = 2 * (W + 4) + 2 * W

36 = 2 * W + 2 * 4 + 2 * W

36 = 2 * W + 8 + 2 * W

36 = 2 * W + 2 * W + 8

36 = 4 * W + 8

-8 -8

28 = 4 * W

/4 /4

7 = W

So, now we have solved for W! We can get L from the given statement that L = W + 4 by plugging in our new value for W.

L = W + 4

L = 7 + 4

L = 11

Let's check with the other equation. We now have W = 7, L = 11, Perimeter = 36, and Perimeter = 2 * L + 2 * W. Let's plug all that information in.

Perimeter = 2 * L + 2 * W

36 = 2 * L + 2 * W

36 = 2 * 11 + 2 * 7

36 = 22 + 14

36 = 36

Wonderful, it all checks out! So, we have found and confirmed that the width of our rectangle is 7 and the length of our rectangle is 11!

Answer 2

given the perimeter of rectangle = 36 feet

formula for perimeter of rectangle = 2(l+w) ==(2l+2w)

given the length = width + 4 feet

i.e l = w+4

substituting in the formula

2( (w+4) + w) = 36

2w+8 + 2w = 36

4w = 36-8 = 28

w = 7

l = 11

so width of rectangle = 7 feet and length = 11 feet.

cross verification :

2( (7+4)+7)= 2(11+7) = 2x18 = 36 feet

Answer 3

Let P be the perimeter of the rectangle and let L and W be the length and width.

P = 2 (L+W)

36 = 2(L + W)

18 = L + W ….equation 1

L = W + 4 ….equation 2, given

substitute value of L from equation 2 to equation 1

18 = W+4+W

18 = 2W + 4

14 = 2W

7 = W

substitute value of W to equation 2

L = 7 + 4

L = 11

Now check the answers

2 ( L + W ) = 2(11+7) = 2(18) = 36.....correct

L = W+4

11 = 7 + 4 ….correct

so answer is Length is 11 and width is 7 feet.