NCERT MATHS CLASS - X
Quadratic Equations
Quadratic Equations
Exercise 4.2
Question 5:
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Let the base of the right triangle be x cm.
Its altitude = (x − 7) cm
Either x − 12 = 0 or x + 5 = 0, i.e., x = 12 or x = −5
Since sides are positive, x can only be 12.
Therefore, the base of the given triangle is 12 cm and the altitude of this triangle will be (12 − 7) cm = 5 cm.
Question 6:
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 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.
Sol.
Let the no. of articles produced be x.
Therefore, cost of production of each article = Rs (2x + 3)
It is given that the total production is Rs 90.
Either 2x + 15 = 0 or x − 6 = 0,
i.e.,
The number of articles produced cannot be a negative integer
Hence, number of articles produced = 6
Cost of each article = 2 × 6 + 3 = Rs 15