CBSE Class 10-Mathematics: Chapter –4 Quadratic Equations Part 9

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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