## anonymous 3 years ago The perimeter of a rectangle is 50 cm and the length is 4 cm longer than the width. Write and solve the system of equations using the substitution method. A. width = 10 cm, length= 14 cm B. width = 10 1/2 cm, length= 14 1/2 cm C. width = 11 cm, length= 15 cm D. width = 23 cm, length= 27 cm

1. anonymous

Do you know the equation for the perimeter of a rectangle?

2. anonymous

|dw:1350324998775:dw|

3. anonymous

There are four sides, so to find the perimeter we just add them all up$perimeter = length + length + width + width$

4. anonymous

we can simplify this expression by using multiplication because $width + width = 2 \times width$

5. anonymous

and $length + length = 2 \times length$

6. anonymous

so the perimeter equation looks like this$perimeter = 2 \times length + 2 \times width$

7. anonymous

this problem gives us two pieces of information that we can insert into out equation for perimeter

8. anonymous

we are told that the perimeter = 50 and that the length is 4 more than the width so we can write the length like this $length = width + 4$

9. anonymous

we can substitute both of these pieces of information into the equation for perimeter$perimeter = 2 \times length + 2 \times width$

10. anonymous

to get:$50 = 2 \times (width + 4) + 2 \times width$

11. anonymous

By substituting length with width + 4 we reduced the equation to a single variabale which we can solve.

12. anonymous

thanks

13. anonymous

can you handle it from here?

14. anonymous

yeah I had after the first two messages, but thanks for being so detailed I appreciate it

15. anonymous

Now how do I give you a medal?