Two possible plans for a new bathroom are shown. Is there a value of x for which the perimeters are equal? Show your work. Explain the reasoning.

There is no value of x to fit this requirement.

Step-by-step explanation:

The 2 perimeters in terms of x are:

4(x + 3) for the square and

2(x+1) + 2(x +4)  for the rectangle

and these need to be equal so

we equate these 2 and solve for x:

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

4x + 12 = 2x + 2 + 2x + 8

4x + 12 = 4x + 10

4x -  4x = 10 - 12

0 = -2   which is of course absurd so there is no solution to this equation.

(x+3)•4=(x+4)•2+(x+1)•2

Step-by-step explanation:

4x+12=2x+8+2x+2

4x-2x-2x=-12+8+2

0=-2

this expression is indeterminate.

x = 25

step-by-step explanation:

a^2+b^2=c^2

7^2+24^2=c^2

49+576=625

sqrt625=25

x=25