CBSE Class 10-Mathematics: Chapter – 4 Quadratic Equations Part 9 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 7:

The diagonal of a rectangular field is meters more than the shorter side. If, the longer side is metres more than the shorter side, find the sides of the field.


Let shorter side of rectangle metres

Let diagonal of rectangle metres

Let longer side of rectangle metres

According to Pythagoras theorem,

Comparing equation with standard form ,

We get and

Applying quadratic formula

We ignore . Since length cannot be in negative.

Therefore, which means length of shorter side metres

And length of longer side metres

Therefore, length of sides are and in metres.

Question 8:

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


Let smaller number and let larger number

According to condition:

Also, we are given that square of smaller number is times the larger number.

Putting equation (2) in (1) , we get

Comparing equation with general form ,

We get , and

Using quadratic formula

Using equation (2) to find smaller number:


Therefore, two numbers are or