If $x^2 - y^2 = 7$ and $x - y = 1$, then the length of a diagonal of a rectangle with length and width respectively x cm and y cm will be -

Explanation

Given that, $x^2 - y^2 = 7$ and $x - y = 1$ .............(i) $(x - y)(x + y) = 7$ $\therefore \quad 1(x + y) = 7$ $x + y = 7$ ..............(ii) On Adding eqⁿ (i) and (ii) $2x = 8$ $x = 4$ and $y = 4 - 1 = 3$ [by putting the value of $x$ in eqn (i)] D C <table> <tr> <td>A B</td> </tr> </table> $x = 4$ $y = 3$ Length of diagonal of rectangle ABCD = $\sqrt{(AB)^2 + (BC)^2}$ = $\sqrt{(4)^2 + (3)^2}$ = $\sqrt{16 + 9} = \sqrt{25} = 5$ cm