1.

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» `sqrt(l^2 + b^2) = b+ 60`
`l =b + 30`
`l^2 + b^2 = b^2 + 3600 + 120b`
`l^2 - 120b - 3600 = 0`
`l^2 = b^2 + 900 + 60b`
`b^2 + 900 + 60b - 120b - 3600 = 0`
`b^2 - 60b - 2700 = 0`
`b^2- 90b + 30b - 2700 = 0`
`b(b-90) + 30(b-90) = 0`
`b= 90, -30`
b cannot be negative, so`b=90`
`l=b+30= 90+30 = 120 m`
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