Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

and \[length + length = 2 \times length\]

Answer 5

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

Answer 6

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

Answer 7

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
\[length = width + 4\]

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

thanks

Answer 12

can you handle it from here?

Answer 13

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

Answer 14

Now how do I give you a medal?