Answer:
Area of rectangle(A) is given by:
[tex]A = lw[/tex]
where,
l is the length and w is the width of the rectangle
As per the statement:
a family is building a rectangular fountain in the backyard. the yard is rectangular and measures 8x by 9x
⇒[tex]\text{Area of yard} = 8x \cdot 9x = 72x^2[/tex]
It is also given that:
The fountain is going to measure 2x by 5x.
[tex]\text{Area of fountain} = 2x \cdot 5x = 10x^2[/tex]
We have to find the area of the remaining yard.
[tex]\text{Remaining area of yard} = \text{Area of yard} -\text{Area of the fountain built}[/tex]
⇒[tex]\text{Remaining area of yard} = 72x^2-10x^2 = 62x^2[/tex] [Combine like term]
Therefore, the area of the remaining yard is, [tex]62x^2[/tex]
