Areas of Similar Triangles

Q.

The line segment XY is parallel to side AC of Δ ABC and it divides the triangle into two parts of equal areas. Find the ratio $\frac{AX}{AB}$.

Q.

The line segment XY is parallel to side AC of $△$ABC and it divides the triangle into two parts of equal areas. Find the ratio $\frac{BX}{AB}$.

1. $\frac{1}{\sqrt{2}}$

2. $\frac{1}{2}$

3. $\frac{4}{\sqrt{1}}$

4. $\frac{\sqrt{2}}{1}$

Q.

The line segment XY is parallel to side AC of Δ ABC and it divides the triangle into two parts of equal areas. Find the ratio $\frac{BX}{AB}$.

1. $\frac{1}{\sqrt{2}}$
2. $\frac{1}{2}$
3. $\frac{4}{1}$
4. $\frac{\sqrt{2}}{1}$

Q. In an equilateral triangleABC, D is a point on side BC such that $BD=\frac{1}{3}$BC. prove that 9AD=7AB.

Q.

The line segment XY is parallel to side AC of Δ ABC and it divides the triangle into two parts of equal areas. Find the ratio $\frac{BX}{AB}$.

Q. If the sides of two similar triangles are in a ratio 2:1, the ratio of their area is _______ .

1. 1:4
2. 4:1
3. 2:1
4. 1:2

Q. The ratio of area of triangle ABC and triangle DEF is 16 : 25. What is the ratio of their height?

1. 4 : 5
2. 16 : 25
3. 5 : 16
4. 16 : 5

Q.

In $\Delta$ABC, if a triangle is formed by joining the midpoints of the sides, the area of the triangle is___ times the area of $\Delta$ ABC.

1. 4

2. 2

3. $\frac{1}{3}$

4. $\frac{1}{4}$

Q.

The areas of two similar triangles are 12 $c{m}^2$ and 48 $c{m}^2$. If the height of the smaller triangle is 2.1 $cm$, then the corresponding height of the bigger triangle is _____.

1. 4.41 cm

2. 8.4 cm

3. 4.2 cm

4. 0.525 cm

Q.

The ratio of the corresponding sides of two similar triangles is 1 : 3. The ratio of their corresponding heights is _________.

1. 1:3

2. 3:1

3. 9:1

4. 1:9

Q. The sides of two similar triangles are in the ratio of 4 : 9. The ratio of their areas is ___ .

1. 9 : 4
2. 4 : 9
3. 81 : 16
4. 16 : 81

Q.

The areas of two similar triangles are $9c{m}^{2}and16c{m}^2$ respectively . The ratio of their corresponding sides is ____.

1. 3: 4

2. 4: 3

3. 2: 3

4. 4: 5

Q. The ratio of the areas of similar triangles is equal to the ratio of their corresponding sides.

1. False
2. True