Scale Factor of Length

Q. Three bus-stops situated at A, B and C in the following figure are operated by handicapped person. These three bus − stops are equidistant from each other. OB is the bisector of ∠ABC and OC is the bisector of ∠ACB.



(i) Find ∠BOC.

(ii) Do you think employment provided to handicapped persons is important for the development of the society? Express your views with relevant points.

Q.

The triangle PQR is reduced to form triangle STU. Calculate the scale factor.

1. 2

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

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

4. Cannot be determined

Q.

If a triangle, with one of its side 7 cm, is enlarged by a scale factor of 4, then find the length of the corresponding side in the new triangle.

1. 22 cm

2. 1.75 cm

3. 10 cm

4. 28 cm

Q. The sides of $\Delta \text{ABC}$ are 6 cm, 8 cm and 10 cm. Find the perimeter of the larger triangle which is similar to $\Delta \text{ABC}$ if the ratio of corresponding sides is 2.

1. 12 cm
2. 36 cm
3. 24 cm
4. 48 cm

Q. One side of an equilateral triangle is 24 cm. The mid - points of its sides are joined to form another triangle whose mid - points are in turn joined to form still another triangle. This process continues indefinitely. Then the sum of the perimeters of all the triangles is

1. $144$cm
2. $212$ cm
3. $288$ cm
4. $172$ cm

Q. $△\text{ABC}\sim \Delta \text{XYZ}$ and the ratio of the corresponding sides of $\Delta \text{XYZ}$ and $\Delta \text{ABC}$ is 2:1. Find the measure of sides XY, YZ and ZX.

Q.
$\text{If}△ABC\sim △PQR,$
then, $\frac{Ar△ABC}{Ar△PQR}=$ .

1. $\frac{p}{b}$
2. $\frac{c^2}{r^2}$
3. $\frac{a}{p}$

Q. The sides of $\Delta \text{ABC}$ are 6cm, 8cm and 10cm. Find the sides of the larger triangle which is similar to $\Delta \text{ABC}$ if the ratio of corresponding sides is 2.

1. 3cm, 4cm and 5cm
2. 12cm, 16cm and 20cm
3. 12cm, 5cm and 13cm
4. None of these

Q.

If a triangle, with one of its side 12 cm, is reduced by a scale factor of $\frac{1}{3}$, then find the length of the corresponding side of the new triangle.

1. 4 cm

2. 48 cm

3. 3 cm

4. 7 cm

Q. Given: $△\text{ABC}\sim \Delta \text{XYZ}$
The ratio of the corresponding sides of $\Delta \text{XYZ}$ and $\Delta \text{ABC}$ is 2:1. Find the measure of sides XY, YZ, and ZX.