Ratio of Areas of Triangles Having Common Vertex and Bases in a Straight Line

Q. Corresponding sides of two similar triangles are in the ratio of 2:3. If the area of the smaller triangles is 48 $c{m}^2$, then find the area of the larger triangle

Q.

In the triangle ACB Line AP divides the two triangles APB and ACP.

If Area of $\Delta$ APB = $24c{m}^2$ and Area $\Delta$ APB : Area of $\Delta$ APC = 4 : 7, find the area of $\Delta$ APC

1. $42c{m}^2$

2. $36c{m}^2$

3. $54c{m}^2$

4. $48c{m}^2$

Q.

Question 66

Most of the sailboats have two sails, the jib and the mainsail. Assume that the sails are triangles. Find the total area of each sail of the sailboats to the nearest tenth.

Q. The height of triangle ABC is 40 cm and its area is 100 $c{m}^2$. In triangle ADE, DE = $\frac{1}{2}$BC. If the areas of these triangles are equal then find height of triangle ADE (in cm).

1. 80

Q. If $\Delta ABC\sim \Delta DEF$, AB = 4cm, DE = 6, EF = 9cm and FD = 12cm, then find the perimeter of $\Delta ABC$.

Q.

The triangle ABC is given.

If CO : OB = 2 : 5 and Area of Triangle AOC = $44c{m}^2$

Find Area of Triangle AOB.

1. $88c{m}^2$

2. $22c{m}^2$

3. $110c{m}^2$

4. $100c{m}^2$

Q.

The triangle ABC has a line AP and the Perpendicular AO.

If Ratio of BO and OC is 10 : 7 and Area of Triangle AOC = $42c{m}^2$ , Find the Area of full triangle ABC

1. $112c{m}^2$

2. $100c{m}^2$

3. $102c{m}^2$

4. $108c{m}^2$

Q. In what ratio does the centroid of the triangle divide each median of the triangle?

1. 2 : 1
2. 5 : 1
3. 3 : 1
4. 4 : 1

Q. The centroid divides each median of the triangle in the ratio 1:2.

1. False
2. True

Q. The ratio of areas of triangles on the same straight line and having common vertices is equal to the ratio of their bases

1. True
2. False