Question

A square plot with a length of 105 yards and an area of 2xsquared. If a rectangular footbal field of the same length with an area of xsquared -30x is made within the plot, find the leftover area of the plot.

Answer 1

7739.44 square yards

Explanation:

Given:

Length of the square plot = 105 yards

Area of square plot =
`2x^2`

Length of rectangular plot is same as square plot.

Area of the rectangular plot =
`x^2-30x`

Now, we know that, area of square is equal to the square of its length.

Therefore, the area of square is given as:

`Area\ of\ square=(length)^2\\\\2x^2=105^2\\\\2x^2=11025\\\\x^2=(11025)/(2)\\\\x=√(5512.5)=74.25\ yd`

Now, area of rectangular field =
`x^2-30x=(74.25)^2-30(74.25)=3285.56\ yd^2`

Now, area of leftover = Area of square plot - Area of rectangular field

∴ Area of leftover = 11025 - 3285.56 = 7739.44 square yards