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