Q:

ANSWER ASAP!! GIVING BRAINLIEST TO FIRST PERSON TO ANSWER BOTH QUESTIONS!!!A square and a rectangle have the same perimeters. The length of a side of the square is 4x-1. The length of the rectangle is 2x+1 and the width is x+2. What is the value of x? What is the perimeter of the square and the rectangle?1. DEFINE YOUR VARIABLE2. WRITE AND EQUATION3. SOLVE THE EQUATION4. WRITE A SENTENCE FOR YOUR SOLUTION

Accepted Solution

A:
Answer:The answer to your question is:x = 1Square's perimeter = 12Rectangle perimeter = 12The value of x is one and the perimeter of the square and the rectangle is the same.Step-by-step explanation:DataSide of Square = 4x - 1Length of rectangle = 2x + 1Width = x + 2Perimeters are the sameProcessSquare perimeter = 4(4x - 1)Rectangle's perimeter = 2(2x + 1) + 2(x+ 2)Then                  4(4x - 1) =  2(2x + 1) + 2(x+ 2)       Equation                  16x - 4 = 4x + 2 + 2x + 4                        16x - 4 = 6x + 6                  16x - 6x = 6 + 4                  10x = 10                  x = 10 / 10                  x = 1       Perimeter of the square = 4(4(1) - 1)                                         = 4(3)                                         = 12Perimeter of the rectangle = 2(2(1) + 1) + 2((1)+ 2)                                             = 2(3) + 2(3)                                             = 6 + 6                                             = 12