R. D. Sharma Solutions for Chapter: Quadratic Equations, Exercise 10: EXERCISE 4.10

The hypotenuse of a right triangle is $25 \mathrm{cm}$. The difference between the lengths of the other two sides of the triangle is $5 \mathrm{cm}$. Find the lengths of these sides.

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.

The hypotenuse of a right triangle is $3\sqrt{10} \mathrm{cm}.$ If the smaller leg is tripled and the longer leg doubled, new hypotenuse will be $9\sqrt{5} \mathrm{cm}.$ How long are the legs of the triangle?

A pole has to be erected at a point on the boundary of a circular park of diameter $13$ meters in such a way that the difference of its distances from two diametrically opposite fixed gates $A$ and $B$ on the boundary is $7$ meters. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?