Manipur Board Solutions for Chapter: Quadratic Equations, Exercise 2: EXERCISE 5.2

The sides containing the right angle of a right triangle are $x$ and $3x+1$ (measured in$\mathrm{cm}$) long. If the area of the triangle is $100 \mathrm{sq}.\mathrm{cm}$, find the lengths of the sides containing the right angle of the right triangle.

The difference between the lengths of the two diagonals of a rhombus is $2 \mathrm{cm}$. If the area of the rhombus is $24 \mathrm{sq}. \mathrm{cm}$, find the length of the sides of the rhombus.

The length of a rectangular plot is $4 \mathrm{m}$ more than its breadth. If the area of the plot is $320 \mathrm{sq}. \mathrm{m}$, find the length and breadth of the plot.

A rectangular looking glass $18 \mathrm{cm}$ by $12 \mathrm{cm}$ has a wooden frame of uniform width. If the area of the frame is equal to that of the looking glass, find the dimensions of the framed glass.

A sum of $₹200$ lent out at compound interest compounded annually amounts to $₹220.50$ in two years. What is the rate of interest in $\%$?

A journey of $224 \mathrm{km}$. from Imphal to Jiribam takes $2\frac{2}{5}$ hours less by a car than by a passenger bus. If the average speed of the bus is $12 \mathrm{km}/\mathrm{hr}$ less than that of the car, find the average speed of the bus and that of the car.

A motorboat whose speed is $18 \mathrm{km}/\mathrm{hr}$ in still water takes $1$ hour more to go $24 \mathrm{km}$ upstream than to return downstream to the same spot. Find the speed of the stream in $\mathrm{km}/\mathrm{hr}$.

The speed of a boat in still water is $8 \mathrm{km}/\mathrm{hr}$. It can go $15 \mathrm{km}$ upstream and $22 \mathrm{km}$ downstream in $5$ hours. Find the speed of the stream in $\mathrm{km}/\mathrm{hr}$.