R. D. Sharma Solutions for Chapter: Quadratic Equations, Exercise 11: EXERCISE 4.11

Two squares have sides $x \mathrm{cm}$ and $(x+4) \mathrm{cm}.$ The sum of their areas is $656 {\mathrm{cm}}^2.$ Find the sides of the squares.

The area of a right-angled triangle is $165 {\mathrm{m}}^2.$ Determine by its base and altitude if the latter exceeds the former by $7 \mathrm{m}$.

Is it possible to design a rectangular mango grove whose length is twice its breadth and the area is $800 {\mathrm{m}}^2$? If so, find its length and breadth.

Is it possible to design a rectangular park of perimeter $80 \mathrm{m}$ and area $400 {\mathrm{m}}^2$. If so, find its length and breadth.

Sum of the areas of two squares is $640 {\mathrm{m}}^2$. If the difference of their perimeters is $64 \mathrm{m}$. Find the sides of the two squares.

Sum of the areas of two squares is $400 {\mathrm{cm}}^2$. If the difference of their perimeters is $16 \mathrm{cm},$ find the sides of two squares.

The area of a rectangular plot is $528 {\mathrm{m}}^2$. The length of the plot (in metres) is one metre more than twice its breadth. Find the length and the breadth of the plot.

In the centre of a rectangular lawn of dimensions $50 \mathrm{m}\times 40 \mathrm{m}$, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be $1184 {\mathrm{m}}^2$. Find the length and breadth of the pond.