Perimeter of a Rectangle: Worded problems

After squaring all sides, we can calculate the area as follows:

$4^2=16$

Since we are given that the area of the square equals the area of the rectangle , we will write an equation with an unknown since we are only given one side length of the parallelogram:

$16=1\times x$

$x=16$

In other words, we now know that the length and width of the rectangle are 16 and 1, and we can calculate the perimeter of the rectangle as follows:

$1+16+1+16=32+2=34$

Since every pair of opposite sides in a rectangle are equal, we know that:

$AB=CD=x+2$

$AD=BC=x$

We can then create the following equation based on the given data:

$30=x+x+2+x+x+2$

$30=4x+4$

$30-4=4x$

$26=4x$

$x=6.5$