Relation between area and sides of similar triangles

Q.

The diagonal of a parallelogram divides it into 2 congruent triangles. State whether true or false.

1. True

2. False

Q.

Find the ratio of area of the equilateral triangles whose sides are 3 and 4 units.

1. 16: 25

2. 9: 16

3. 9 : 25

4. None of the above

Q.

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

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

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

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

4. All of the above.

Q.

In the given figure, by how much should the length of DC be increased so that $△$ ABC $\cong$ $△$ DBC?

Given that AB= 6 cm, AC= 5cm, BC= 4cm and BD= 6cm.

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1. 3 cm

2. 5 cm

3. 2 cm

4. 6 cm

Q.

The sides of two similar triangles are in the ratio $4:9$. Find the ratio of areas of these triangles.

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.

__

Q.

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

__

Q.

In the given figure, ABCD is a parallelogram with x : y = 1 : 1 and OE || AD. Then, (area of $\Delta ADC$ + area of $\Delta BOC$) : area of $\Delta ODC$ is

1. 4 : 1

2. 9 : 1

3. 16 : 1

4. None of the above

Q.

In an equilateral $△ABC$, if $△DFE$ is formed by joining the midpoints of the sides, the area of $△DFE$ is ___ $\times$ the area of $△$ ABC.

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

Q.

$ABCD$ is a square. Equilateral triangles $ACF$ and $ABE$ are drawn on the the diagonal $AC$ and side $AB$ respectively. Find area of $△ACF$ : area of $△ABE$.

1. $\sqrt{2}:1$

2. $2:1$

3. $4:1$

4. $8:1$

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.

The corresponding sides of 2 similar triangles $△ABC$ and $△PQR$ are in the ratio 5:2. Given that AB=3 cm and AC=10 cm, the length of side PR (in cm) is___________.

1. 5cm

2. 6cm

3. 4cm

4. 3cm

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. 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. In the given figure, DE || BC and AD : DB = 5 : 4, then $\frac{areaof\Delta DOE}{areaof\Delta DCE}$ is

1. 15 : 4
2. 25 : 16
3. 5 : 14
4. 25 : 196

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.

In this figure, ABCD is a trapezium in which AB || DC and AB = 3DC. Determine the ratio of the areas of $△$ AOB and $△$COD.

1. 9 : 1

2. 3 : 4

3. 16 : 1

4. 4 : 1

Q.

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

1. 4: 5

2. 3: 2

3. 5: 4

4. 5: 7

Q.

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

1. 2: 3

2. 4: 3

3. 3: 4

4. 4: 5

Q. In a right angle triangle $\Delta ABC$, a perpendicular BD is drawn on to the largest side from the vertex B. Which of the following does NOT give the ratios of the areas of $\Delta ABD$ and $\Delta BCD$ ?

1. ${\left(\frac{AB}{BC}\right)}^2$
2. ${\left(\frac{AB}{AC}\right)}^2$
3. ${\left(\frac{BD}{DC}\right)}^2$
4. ${\left(\frac{AD}{BD}\right)}^2$

Q.

D and E are points on the sides AB and AC respectively of a $△$ABC such that DE || BC and DE divides $△$ABC into two parts that are equal in area. Find $\frac{BD}{AB}$.

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

2. (a) and (b) above.
3. None of the above

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

Q. Find the ratio of the areas of two similar triangles $\Delta ABC$ and $\Delta PQR$ shown in the figure.

1. ${\left(\frac{AB}{PQ}\right)}^2$
2. ${\left(\frac{BC}{QR}\right)}^2$
3. ${\left(\frac{AC}{PR}\right)}^2$
4. $Allofthese$

Q. In a right angle triangle $\Delta ABC$, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of $\Delta ABD$ and $\Delta BCD$?

1. ${\left(\frac{AD}{BD}\right)}^2$
2. ${\left(\frac{BD}{DC}\right)}^2$
3. ${\left(\frac{AB}{BC}\right)}^2$
4. ${\left(\frac{AB}{AC}\right)}^2$

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. $\frac{36}{49}$

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

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