Telangana Board Solutions for Chapter: Quadratic Equations, Exercise 5: Exercise

Find two consecutive positive integers, sum of whose squares is $613.$

The altitude of a right triangle is $7 \mathrm{cm}$ less than its base. If the hypotenuse is $13 \mathrm{cm},$ find the other two sides.

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 $\mathrm{Rs} 90,$ find the number of articles produced and the cost of each article.

Find the dimensions of a rectangle whose perimeter is $28 \mathrm{meters}$ and whose area is $40 \mathrm{square} \mathrm{meters}$

The base of a triangle is $4 \mathrm{cm}$ longer than its altitude. If the area of the triangle is $48 \mathrm{sq}.\mathrm{cm}$ then find its base and altitude.

Two trains leave a railway station at the same time. The first train travels towards west and the second train towards north. The first train travels $5 \mathrm{km}/\mathrm{hr}$ faster than the second train. If after two hours they are $50 \mathrm{km}$ apart, find the average speed of each train.

In a class of $60$ students, each boy contributed rupees equal to the number of girls and each girl contributed rupees equal to the number of boys. If the total money then collected was $₹1600.$ How many boys were there in the class?

A motor boat heads upstream a distance of $24 \mathrm{km}$ in a river whose current is running at $3 \mathrm{km} \mathrm{per} \mathrm{hour}.$ The trip up and back takes $6 \mathrm{hours}.$ Assuming that the motor boat maintained a constant speed, what was its speed in still water?