M L Aggarwal Solutions for Chapter: Quadratic Equations, Exercise 1: EXERCISE 6.1

The sum of two numbers is $9$ and sum of their squares is $41$. Taking one number as $x$, form an equation in $x$ and solve it to find the numbers.

The sum of the squares of two consecutive positive even integers is $340$. Find the integers.

A two digit number is four times the sum and three times the product of its digits. Find the number.

The hypotenuse of a right angled triangle is $17 \mathrm{cm}$ and the difference between the other two sides is $7 \mathrm{cm}$ long. Find the lengths of the two unknown sides.

Originally a rectangle is twice as long as it is wide. When $4 \mathrm{m}$ were added to its length and $3 \mathrm{m}$ subtracted from its width, the resulting rectangle had an area of $600 {\mathrm{m}}^2$. Find the dimensions of the new rectangle.

A rectangular garden of dimensions $10 \mathrm{m} \times 16 \mathrm{m}$ is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is $120 \mathrm{Sq}.\mathrm{m}$, find its width.

Two years ago, a man's age was three times the square of his son's age. In three years time, his age will be four times his son's age. Find their present ages.

A piece of cloth costs $₹175$. If the piece were $4 \mathrm{m}$ longer and each metre costs $₹5$ less, the cost would have remained unchanged. How long is the piece?