Question

Geometry:sammie bought just enough fencing to border either a rectangular plot or a square plot, as shown. The perimeters of the plots are the same. How many meters pf fencing did she buy?

Answer 1

Answer is 12 meters of fencing

First our equation.

We know perimeter is 2x length + 2x width.
We know the perimeters of both plots are the same so they equal each other.

Square = 4 sides by ( x + 2)

Rectangle = 2 sides by (3x + 2) and 2 by (x-1).

Your equation

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

Distributive multiply

4x + 8 = 6x + 4 + 2x -2

Combine like terms

4x +8 = 8x +2

We want to isolate the variable x on one side and numbers on the other side of = sign.

Subtract 8 from both sides

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

4x = 8x -6

Now subtract 8x from both sides

4x -8x = -6

-4x = -6

Divide both sides by -4 to solve for x

-4/-4 x = -6/-4

X = 1-1/2 or 1.5 m

Now substitute your x value into each of the equations (plot sides) to get your answers.

Square = 4 (x + 2)
4 (1.5 x 2)
4( 3) = 12m

Rectangle = one side is 2(3x +2)
2 (3*1.5 +2)
2(4.5 +2)
9+2 = 11

The other side is 2(x-1)
2 (1.5 -1)
2(.5) = 1

Rectangle = 11 + 1 = 12m
Square = 12m

Problem solved!