The perimeter of a rectangle is 64cm. the length is 4 cm less than twice the width. find the length and width.

Hello there!

Your answer is:

Length = 20

Width = 12

Explanation and Work:


To solve this, we must make a system of equations.

2L + 2W = 64

L = (2W-4)

Now, we must plug (2W-4) into the first equation for l

2(2W-4) + 2w = 64

2 * 2w = 4w 

2 * -4 = -8

4w - 8 + 2w = 64

6w - 8 = 64

Now let's solve this

6w - 8 = 64
     +8    +8

6w = 72

Now, divide 72 by 6

72/6 = 12

w = 12

Now, we must plug 12 into the second equation into the w.

L = (2W-4)

L = 2 * 12 - 4

L = 24 - 4

L = 20

So, we know that L = 20 and w = 12

That means

Length = 20

Width = 12

Now, let's check this.

(12 * 2) + (20 * 2) = 64

12 * 2 = 24

24 + (20 * 2) = 64

20 * 2 = 40

24 + 40 = 64

24 + 40 = 64

64 = 64

I hope I helped!

~ Fire