A square and rectangle have the same perimeter. Find the sides lengths of each. The square is (x+1) and the rectangle is (2x+3) and (x-1)

Question

Please help me solve this question

Answer 1

For this question, you defined one side of the square to be (x+1). Therefore, if you calculated the perimeter, then you would add all four sides together. This gives you (x+1) + (x+1) + (x+1) + (x+1) or 4(x+1). 

 

You also stated that the rectangle has a side with value (2x+3) and a side value (x-1). Therefore, if we calculate the perimeter again, we should get (2x+3) + (2x+3) + (x-1) + (x-1) or 2(2x+3) + 2(x-1).

 

We know that the square and the rectangle have the same perimeter, therefore:

4(x+1) = 2(2x+3) + 2(x-1)

 

Use the distributive property and get all your like terms on one side of the equation, and solve! :)