CBSE Class 10-Mathematics: Chapter –4 Quadratic Equations Part 8

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Question 4:

The altitude of right triangle is less than its base. If, hypotenuse is . Find the other two sides.

Answer:

Let base of triangle be and let altitude of triangle be

It is given that hypotenuse of triangle is

According to Pythagoras Theorem,

Dividing equation by

We discard because length of side of triangle cannot be negative.

Therefore, base of triangle

Altitude of triangle

Question 5:

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that cost of production of each article (in rupees) was more than twice the number of articles produced on that day. If, the total cost of production on that day was Rs. 90, find the number of articles produced and the cost of each article.

Answer:

Let cost of production of each article be Rs

We are given total cost of production on that particular day

Therefore, total number of articles produced that day

According to the given conditions,

Cost cannot be in negative, therefore, we discard

Therefore, which is the cost of production of each article.

Number of articles produced on that particular day

Question 6:

In a class test, the sum of Shefali’s marks in Mathematics and English is . Had she got marks more in Mathematics and marks less in English, the product of their marks would have been . Find her marks in the two subjects.

Answer:

Let Shefali’s marks in Mathematics

Let Shefali’s marks in English

If, she had got marks more in Mathematics, her marks would be

If, she had got marks less in English, her marks in English would be

According to given condition:

Comparing quadratic equation with general form

We get

Applying Quadratic Formula

Therefore, Shefali’s marks in Mathematics or

Shefali’s marks in English

Or Shefali’s marks in English

Therefore, her marks in Mathematics and English are or .