Question

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

Answer 1

Let shorter side in meters `= x `
Then, longer side in meters`=x+30`
Then, diagonal in meters `=x+60`
Now, from pythagoras theorem,
`x^2+(x+30)^2 = (x+60)^2`
`=>x^2+x^2+900+60x = x^2+3600+120x`
`=>x^2-60x-2700 = 0`
`=>x^2-90x+30x-2700 = 0`
`=>(x-90)(x+30) = 0` `=> x= 90 or x=30`
As, side of rectangle can not be negative. So, `x = 90`.
Thus, sides of rectangle are `90 and 120` metres.