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

Question

What is x and the equation

 

Answer 1

Square Perimeter = 4(4x-1)

Rectangle Perimeter = 2(2x+1) + 2(x+2)

 

Square Perimeter = Rectangle Perimeter

4(4x-1) = 2(2x+1) + 2(x+2) 

16x - 4 = 4x + 2 + 2x + 4

16x - 4 = 6x + 6

-6x  +4  -6x  +4

10x = 10

x = 1

 

Answer 2

Since the perimeters are equal, we know that:

 

perimeter of square = perimeter of rectangle

 

now plug in the appropriate perimeter formulas.

 

for a square, P =4s. For a rectangle, P = 2l +2w

 

4s = 2l + 2w. ,  insert the expressions for s, l and w

 

4(4x-1) = 2(2x+1) + 2(x+2).  This is the equation.

 

16x-4 = 4x+2+2x+4.   

16x-4 = 6x+6

10x=10

x=1

Answer 3

4x - 1 = side of square

 

2x + 1 = length of rectangle

x + 2 = width of rectangle

Since their perimeters are equal,

 

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

 

16x - 4 = 4x + 2 + 2x + 4

10x = 10

x = 1

If we plug 1 in for x,

Each side of the square is 4(1) - 1 = 3

The perimeter is thus 12

 

The length of the rectangle = 2(1) + 1 = 3

The width of the rectangle is 1 + 2 = 3

The perimeter is this 2(3) + 2(3) = 12

 

So x = 1 is the verified.