Calculating perimeter of square and rectangle

Question

A square and rectangle have the same perimeter. The square has a side length of 12x units. The rectangle has a length of (4x +3) units and a width of 7 units. What will be the length of the rectangle?

Answer 1

Hello!

I normally like to draw these things out, but because I can't on here I will try to explain the best I can.

The square has a perimeter of 4*s (side length), this has a side length of 12x, so it's perimeter is 4 * 12x or 48x.

A rectangle has a perimeter of 2L + 2W. Plugging in L = 4x+3 and W = 7, we get

2 (4x+3) + 2(7). Can you simplify this? (Hint: Distribute, then combine like terms.)

Since the square and the rectangle have the SAME perimeter, we can set them equal to each other. So,

48x = 2 (4x+3) + 2(7) Solve for x.

Remember x is not your final answer. Look at what the question is asking for. It's asking for the rectangle length. THe rectangles length was 4x+3. Once you know what x is, just plug it in!

Check it!

Plug in x for all the variables and find the perimeter of each. Are they the same? They should be! Great job!

If you have any questions just let me know.

Answer 2

12x4=2(4x+3)+2*7

48x=8x+6+14

48x=8x+20

40x=20

x=.5

24=24

Answer 3

"SAME PERIMETER": Imagine a string that is used to form the square and then used again to form the rectangle.

Perimeter = 4 * 12x = 2 * (4x+3) + 2 * 7

48x = 8x + 6 + 14

40x = 20

x = 1/2

The length of the rectangle is (4x+3)

4(1/2) + 3

2 + 3

5

The length of the rectangle is 5 units.