Ratio of Area of Any Two Triangles

Q. If the ratio of the corresponding sides of two similar triangles is $1:2,$ then the ratio of their corresponding heights is:

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

Q.

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

1. 3:1

2. 1:9

3. 9:1

4. 1:3

Q.

The perimeter of two similar triangles are 72 cm and 56 cm respectively. If one side of the first triangle is 18 cm, then the corresponding side of the smaller triangle is:

1. 16 cm

2. 18 cm

3. 14 cm

4. 12 cm

Q.

Base of a triangle is 9 cm and the height is 5 cm. Base of another triangle is 10 cm and height is 6 cm. Find the ratio of areas of these triangles.

1. $\frac{3}{4}$
2. $\frac{5}{7}$
3. $\frac{3}{2}$
4. $\frac{1}{4}$

Q.

In similar triangles,

I. The corresponding angles are equal.

II. The corresponding sides are always equal.

III. The corresponding sides are always proportional.

1. Only 1 is true

2. Only 1 & 3 are true

3. Only 1 & 2 are true

4. All the statements are true

Q.

Are the following figure always, sometimes, or never similar?

Explain.

1. two triangles.
2. two squares.
3. two rectangles

Q.

Two sides of a triangle are $10cm$ and $15cm$and the base is $20cm$ long. If another triangle similar to the first triangle has the base measuring $32cm,$find the other two sides of the triangle

Q. Base of a triangle is 9 cm and the height is 5 cm. Base of another triangle is 10 cm and height is 6 cm. Find the ratio of areas of these triangles.

Q. Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of the other triangle. Are the two triangles similar? Why?

Q.

Given $△$ DEF $\sim$ $△$ABC. If AB = 4 cm, BC = 2 cm, CA = 3 cm and EF = 4 cm, then the perimeter of $△$DEF is ____ cm.

1. 18

2. 15

3. 16

4. 14

Q. Minimum number of pairs of equal corresponding angles to make two triangles similar = .

1. 2
2. 3
3. 1

Q. $\Delta ABC\sim \Delta PQR$ and $\frac{AB}{PQ}=2$. Then $\frac{AC}{PR}=$

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

Q. Area of two congruent triangles ABC and PQR are X and Y respectively.
Which of the following is correct?

1. X > Y
2. X < Y
3. X = Y
4. Comparison cannot be done.

Q. The ratio of the areas of two similar triangles is $25:16$. The ratio of their perimeters is ..............

1. $625:256$
2. $5:6$
3. $25:16$
4. $5:4$

Q. A triangle has a base $6cm$ and has the same area as a circle of radius $6cm$ the altitude of the triangle in cm is .......

Q. Two triangles with equal corresponding sides are always similar.

1. False
2. True

Q. Two isosceles triangles have equal vertical angles and their areas are in the ratio 25:49. Ratio of their corresponding heights will be 5:7.

1. False
2. True

Q.

If triangle ABC is an isosceles triangle in which AB = AC = 13 cm, then find the value of $\frac{\text{area of}\Delta ADC}{\text{area of}\Delta EFB}.$ (upto two decimal places)

1. 0.52

Q. Two triangles with equal corresponding sides are always similar.

1. True
2. False