The area of Square C is the square of the height of the Rectangle B.
Correct responses:
- [tex]\underline{Area \ of \ square \ C = \dfrac{\left(Area \ of \ Rectangle \ B \right)^2}{Area \ of \ Square \, A} }[/tex]
- [tex]Area \ of \ square \ C = \underline{\dfrac{16}{7}} \, ft.^2[/tex]
Methods used for finding the area of Square C
The given area of square A = 7 ft.²
The given area of rectangle, B = 4 ft.²
Let s represent the side length of square C and let S represent the side length of square A, we have;
Area of rectangle B = S × s = S·s
Area of square A = S × S = S²
Area of square C = s × s = s²
[tex]\mathbf{\dfrac{(Area \ of \ rectangle \ B)^2}{Area \ of \ square \ A } } = \dfrac{\left(S \cdot s \right)^2}{S^2} = \dfrac{S^2 \cdot s^2}{S^2} = s^2 = Area \ of \ square \ C[/tex]
Therefore, the expression for the area of Square C in terms of the area
of Square A and Rectangle B is presented as follows;
- [tex]\underline{Area \ of \ Square \ C = \dfrac{ \left (Area \ of \ rectangle \ B \right)^2}{\left(Area \ of \ square \ A\right)}}[/tex]
Which gives;
- [tex]\underline{Area \ of \ square \ C = \dfrac{\left(4 \, ft.^2 \right)^2}{7 \, ft.^2}}[/tex]
By simplification, we have;
[tex]\mathbf{\dfrac{\left(4 \, ft.^2 \right)^2}{7 \, ft.^2}} = \dfrac{16}{4} \, ft.^2[/tex]
- [tex]Area \ of \ square \ C = \underline{ \dfrac{16}{7}} \, ft.^2[/tex]
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