Relation between Area and Sides of Similar Triangles

Q.

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

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

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

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

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

Q.

In the given figure, $△ABC\sim △$PQR and AM and PN are medians of $△$ABC and $△$PQR respectively. Then $\frac{Areaof△ABC}{Areaof△PQR}$ = _____

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

2. $\frac{{AM}^2}{{PN}^2}$

3. (a) and (b) above.
4. $\frac{{PQ}^2}{{QR}^2}$

Q. If $\Delta$ABC and $\Delta$PQR are two similar triangles shown in the figure. AM and PN are the medians on $\Delta$ABC and $\Delta$ PQR respectively. Then which of the following statements is true?

1. $\Delta ABM\sim \Delta PQR$
2. $\Delta AMC\sim \Delta PNR$
3. $\Delta ABM\sim \Delta PQN$
4. $\Delta ABM\sim \Delta PNQ$

Q. Let $△ABC\sim △DEF$ and their areas be $64c{m}^2$ and $121c{m}^2$ respectively. If $EF=15.4cm$, find $BC$.

Q. If the ratio of the corresponding sides of two similar triangles is $3:4$, then the ratio of their perimeters is:

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

Q. The areas of two similar triangles are $49{cm}^2$ and $64{cm}^2$ respectively. The ratio of their corresponding sides is:

1. $49:64$
2. $7:8$
3. none of these
4. $64:49$

Q. In $\Delta ABC$, AB = AC and AD is perpendicular to BC. State the property by which $\Delta ADB\cong \Delta ADC$.

1. SSS property
2. SAS property
3. RHS property
4. ASA property

Q. In a $\Delta ABC$, $D$ and $E$ are points on the sides $AB$ and $AC$ respectively such that $DE||BC$.
If $AD=4x-3,AE=8x-7,BD=3x-1$ and $CE=5x-3$, find the value of $x$.

Q. D, E, and F are the mid-points of the sides BC, CA and AB, respectively of a $\Delta ABC$. Then find the ratio of the areas of $\Delta DEF$ and $\Delta ABC$.

Q. In figure, $ABCD$ is a parallelogram
Prove that $\frac{DP}{PQ}=\frac{DC}{BQ}$

Q.

D, E and F are respectively the mid-points of the sides BC, CA and AB of a $△$ABC. Show that
(i) BDEF is a parallelogram.(ii) ar ($△$DEF) = $\frac{1}{4}$ ar ($△$ABC). [4 MARKS]

Q. If the sides of a parallelogram touch a circle. Prove that the parallelogram is a rhombus.

Q. If $\Delta ABC$ and $\Delta PQR$ are two similar triangles shown in the figure. AM and PN are the medians on $\Delta ABC$ and $\Delta PQR$respectively. The ratio of areas of $\Delta ABC$ and $\Delta PQR$ is 9:25. If AM = PO = 5 cm. Find the value of 3(ON) in cm ___

Q. D, E, and F are the mid-points of the sides BC, CA and AB, respectively of a $\Delta ABC$. Then find the ratio of the areas of $\Delta DEF$ and $\Delta ABC$.