Two sides of a plot measure 32 metres and 24 metres and the angle between them is a perfect right angle. The other two sides measure 25 metres each and the other three angles arc not right angles. What is the area of the plot?

Options

A. 168
B. 534
C. 696.5
D. 684

Answer

D

Explanation

`(32-y)^2+(24-x)^2=625 …(1)`
`x^2+y^2=625 …(2)`
`rArr (24)^2+(32)^2-64y-48x=0 ("Form "(1) & (2))`
`rArr 64y+48x=576+1024`
`rArr 4y+3x=36+64=100`
or `y=((100-3x)/4)`
`:. X^2+((100-3x)/4)^2=625` (Form (2))
`rArr -600x+10000+9x^2=625xx16`
`25x^2-600x+10000-625xx16=0`
`rArr x=24and y=7`
`:. "Area" =1/2(24xx25)+1/2(32xx24)=684`