The diagonal of a rectangular field is 16 m more than the shorter side. If the longer side is 14 m more than the shorter side then find the lengths of the sides of the field.

Explanation

Let the shorter side of the field be x metres.
Then, longer side `=(x+14)m.`
And, diagonal `=(x+16)m.`
`:." "(x+16)^(2)-(x+14)^(2)=x^(2)`

`implies" "(2x+30)xx2=x^(2)impliesx^(2)-4x-60=0`
`implies" "x^(2)-10x+6x-60=0impliesx(x-10)+6(x-10)=0`
`implies" "(x-10)(x+6)=0impliesx-10=0" or "x+6=0`
`implies" "x=10" or "x=-6`
`implies" "x=10" "[because" breadth cannot be negative"]`
`:." ""breadth "=10 m" and length "=(10+14)m=24m.`