Andhra Pradesh Board Solutions for Chapter: Similar Triangles, Exercise 11: EXERCISE - 8.3

Equilateral triangles are drawn on the three sides of a right-angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

Prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangles described on its diagonal.

$D, E, F$ are mid points of sides $BC, CA, AB$ of $△DEF$. Find the ratio of areas of $△DEF$ and $△ABC$.

In $△ABC, XY\parallel AC$ and $XY$ divides the triangle into two parts of equal area. Find the ratio of $\frac{AX}{XB}$.

Prove that the ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding medians.

$△ABC~△DEF$. $BC=3 \mathrm{cm}, EF=4 \mathrm{cm}$ and area of $△ABC=54 {\mathrm{cm}}^2$. Determine the area $△DEF$.

$ABC$ is a triangle and $PQ$ is a straight line meeting $AB$ in $P$ and $AC$ in $Q$. If $AP=1 \mathrm{cm}$ and $BP=3 \mathrm{cm},$ $AQ=1.5 \mathrm{cm}$ and $CQ=4.5 \mathrm{cm}$. Prove that $ar\left(△APQ\right)=\frac{1}{16}\times ar\left(△ABC\right)$.

The area of two similar triangles are $81 {\mathrm{cm}}^2$ and $49 {\mathrm{cm}}^2$ respectively. The altitude of the bigger triangle is $4.5 \mathrm{cm}$. Find the corresponding attitude of the smaller triangle.