(Q24)The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 meters more than the shorter side, find the sides of the field.

Let the shorter side of the rectangular field = x m.

Then its longer side = x + 30 m

xx+60x+30

The diagonal of a rectangle is also the hypotenuse of the lower triangle Here the diagonal = x + 60

∴ By Pythagoras theorem

(side)2 + (side)2 = (hypotenuse)2

(x + 30)2 + x2 = (x + 60)2

x2 + 60x + 900 + x2 = x2 + 120x + 3600

x2 - 60x - = 0

x2 - x + 30x - = 0

x(x - ) + 30(x - ) = 0

(x - )(x + 30) = 0

x - = 0 or x + 30 = 0

x = or x = -30 But 'x' can't be negative.

∴ x = m

i.e , the shorter side x = 90 m Longer side x + 30 = +30=m