# 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.

**Answer**:

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.

**Answer**:

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:

And,

Therefore, two numbers are or