Ratio of Area of Similar Triangles

Q. In the given figure, if $PM=10cm,$ $A\left(△PQS\right)=100sqcm,$ and $A\left(△QRS\right)=110sqcm$, then find the measure of $NR$.
[2 Marks]

Q.

If D, E, F are the midpoints of sides BC, CA and AB of $△$ ABC, then the ratio of the area of $△$ DEF to $△$ ABC is:

1. 1: 4

2. 1: 2

3. 2: 3

4. 4: 5

Q.

If the sides of two similar triangles are in the ratio of 4 : 9, then the areas of these triangles are in the ratio ____.

1. 2 : 3

2. 4 : 9

3. 81 : 16

4. 16 : 81

Q.

Two isosceles triangles have equal angles and their areas are in the ratio 16 : 25. The ratio of corresponding heights is :

1. 5: 4

2. 3: 2

3. 5: 7

4. 4: 5

Q.

In given figure $△$ ABC and $△$ DEF are similar, BC = 3cm, EF = 4cm, and area of triangle ABC = 54$c{m}^2$ find the area of $△$ DEF

__ $c{m}^2$

Q.

If $△ABC\sim △$ DEF such that AB = 12 cm and DE = 14 cm. Find the ratio of areas of $△$ ABC and $△$ DEF.

1. $\frac{25}{49}$

2. $\frac{49}{16}$

3. $\frac{36}{49}$

4. $\frac{49}{9}$

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. 4: 5

4. 2: 3

Q.

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

1. $8.4cm$

2. $4.2cm$

3. $0.525cm$

4. $4.41cm$

Q.

$\text{In the given figure,}△ABC\sim △PQR.\text{Then,}\frac{areaof△ABC}{areaof△PQR}\text{equals}$

1. All of the above.

2. $\frac{{AB}^2}{{PQ}^2}$

3. $\frac{{BC}^2}{{QR}^2}$

4. $\frac{{AC}^2}{{PR}^2}$

Q.

$△$ABC and $△$PQR are two similar triangles as shown in the figure such that $\frac{AreaofABC}{AreaofPQR}$ = $\frac{9}{25}$. AM and PN are the medians on $△$ABC and $△$PQR respectively. If AM = PO = 5 cm, find the value of 3ON.

__