Question

What is the value of x that makes the perimeters equivalent?

Answer 1

Answer:

x=5

Step-by-step explanation:

First you want to simplify each shape's perimeter formula.

In this case, we'll call the rectangle A and the triangle B.

1) Address the information (L=Length, W=Width)

A= 2L+2W

B= 2L + W

(Now you add in the information)

A= [2(3x-3) + 2(x-3)]

B= [2(2x-1) +2x]

2) Start to Solve (start by multiplying the 2s by the parentheses)

A=6x-6 +2x-6

B= 4x-2 +2x

3) Combine Like Terms

A= (6x+2x) + (-6 +-6) -> 8x-12

B= (4x+2x) -2 -> 6x-2

4) Now that you've simplified, set both areas as equals to Solve for x

8x-12=6x-2

5) Combine Like Terms. Start by subtracting 6x over. (You subtract to cancel out the positive 6x on the one side, so you can bring it over as a negative)

8x-12=-2

-6x

2x-12=-2

6) Combine Like Terms. Add 12 to both sides (to cancel out the one side's 12)

2x=-2

+12

7) Solve for x.

2x=10

2. 2

x=5

If unsure of answers, you can also plug your answer into the formula to see if your answer was correct. In this case, both shapes have a perimeter of 28.