91Ó°ÊÓ

Find two numbers whose sum is 27 and product is 182 .

Find two consecutive positive integers, sum of whose squares is 365 .

The altitude of a right triangle is \(7 \mathrm{~cm}\) less than its base. If the hypotenuse is \(13 \mathrm{~cm}\), find the other two sides.

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.

The difference of squares of two numbers is 180 . The square of the smaller number is 8 times the larger number. Find the two numbers.

A train travels \(360 \mathrm{~km}\) at a uniform speed. If the speed had been \(5 \mathrm{~km} / \mathrm{h}\) more, it would have taken 1 hour less for the same journey. Find the speed of the train.