Question

The diagonal of a rectangular field 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides the field.

Answer 1

Let, ABCD be the rectangle
and Shorter side BC=x meter
`because` Diagonal AC= (x-60) m
and longer side AB=(x+30) m
Now, in `DeltaABC` by Pythagoras theorem
`(x+60)^(2)=(x=+30)^(2)+x^(2)`
`impliesx^(2)+120x+3600=x^(2)+60x+900+x^(2)`
`impliesx^(2)-60x-2700=0`
`impliesx^(2)-(90-30)x-2700=0`
`impliesx^(2)-90x+30x-2700=0`
`x(x-90)+30(x-90)=0`
`implies(x-90)(x+30)=0`
`impliesx-90=0orx+30=0`
`impliesx=90" "(because"sind cannot be negative")`
Hence, breadth of rectangle = 90 m and length =90+30=120 m.