Answer :
first solve for the perimeter of the rectangle
2w + 2l = 42
since the length of the rectangle is twice as long as the length and width of the square
2w = l
solve using substitution
2w + 2(2w) = 42
2w + 4w = 42
6w = 42
w = 7
are is length x width. a square has the same length and width
7 x 7 = 49
the area of one square is 49
The area of one square is 49 square inches.
What is a square?
A square is a two-dimensional figure and a four-sided polygon which has it's all sides equal in length and the measure of the angles are 90 degrees. The total interior angle is 360 degrees.
For the given situation,
The figure is made up of two identical squares. So it forms a rectangle.
Let width be x then length be 2x.
Perimeter of rectangle = 42 inches
The formula of perimeter of rectangle is
⇒ [tex]P=2(l+w)[/tex]
⇒ [tex]42=2(x+2x)[/tex]
⇒ [tex]42=2x+4x[/tex]
⇒ [tex]42=6x[/tex]
⇒ [tex]x=\frac{42}{6}[/tex]
⇒ [tex]x=7[/tex]
Thus one side of the square is 7 inches.
So formula of area of square is
⇒ [tex]Area = (side)^{2}[/tex]
⇒ [tex]Area = (7)^{2}[/tex]
⇒ [tex]Area = 49[/tex]
Hence we can conclude that the area of one square is 49 square inches.
Learn more about squares here
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