Questions

Construct a triangle having one angle equal to 45$^{\circ}$ and equal in area to the parallelogram ABCD having BC = 5 cm and AB = 4 cm and $\angle$B=60$^{\circ}$.

Construct a $\triangle$ABC in which b = 5 cm, c = 4.8 cm and $\angle$ABC=45$^{o}$. Construct a parallelogram CDEF equal in area to $\triangle$ABC and having a side (CD) = 7.5 cm.

Construct a $\triangle$ABC in which a = 7.8 cm b = 7.2 cm and c = 6.3 cm. Construct a parallelogram equal in area to $\triangle$ABC and having a side 8 cm. 

Construct a triangle ABC in which AB = 6 cm, BC = 7.2 cm, and $\angle$B = 60$^{o}$. Construct a parallelogram equal in area to the triangle ABC with an angle 60$^o$.

Construct a $\triangle$ABC in which BC = 6 cm AC = 5.6 cm and AB=7.6 cm. Construct a parallelogram equal in area to $\triangle$ABC and having an angle 75$^o$.

Solve: $\rm 4^{x} + \frac{1}{4^{x}} = 16 \frac{1}{16}$.

Simplify: $\rm \frac{x + y}{x - y} - \frac{x - y}{x + y}$.

The perimeter and area of a rectangular ground are 66 m and 260 sq.m. respectively.

1. Illustrate the roots of x in the quadratic equation $\rm ax^{2} + bx + c = 0$, $\rm a \neq 0$.
2. Find the length and breadth of the given ground.
3. How many pieces of land can be made with dimension (13×4) square meter from that rectangular field? Calculate it.

There are 3 geometric means between 3 and 243.

1. First term 'a', last term 'b', and the number of geometric means 'n' are given. Write the formula for the calculation of the common ratio in the given condition.
2. What is the third mean of the given series? Find it.
3. In arithmetic mean and geometric mean between 3 and 243, which one is greater and by how much? Compare it.

The length, breadth, and height of a rectangular room are 14 ft, 13 ft, and 10 ft respectively. There are two square windows with 3 feet edges and two doors of size 6ft × 3ft in the room.

1. How much does it cost to paint four walls and ceiling of the room excluding doors and windows at the rate of Rs. 36 per square foot? Find it.
2. How much the total cost will increase to paint on the same part if the cost of painting per square meter is increased by one-third of what it was before due to the increase in the market price? Find it.