Question

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.

Answer 1

(x+3)•4=(x+4)•2+(x+1)•2

Explanation:

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

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

0=-2

this expression is indeterminate.

Answer 2

There is no value of x to fit this requirement.

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.