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# Form 2 Similarity and Enlargement Topical Questions and Answers

Form 2 Similarity and Enlargement Topical Questions and Answers

Lessons (**25**)

- 1.
Points A (4, 2), B (9, 2), C(7, -2) and D (2, -2) are the vertices of a parallelogram. Taking the origin as the centre of enlargement, find the image when the scale factor is -1

9m 3s - 2.
Points A (4, 2), B (9, 2), C(7, -2) and D (2, -2) are the vertices of a parallelogram. Taking the origin as the centre of enlargement, find the image when the scale factor is - #1/4#.

10m 29s - 3.
State the centre of enlargement and the linear scale factor in each of the following figures if #triangle# A'B'C' is the image of #triangle# ABC:

3m 26s - 4.
In #triangle# ABC, AB = 3 cm, BC = 4 cm and AC = 5 cm. The sides AB, BC and AC are enlarged by a linear scale factor of 2.5. Find the length of the new triangle.

2m 34s - 5.
If a road 8 km long is represented by 4 cm on a map, find the scale of the map.

1m 28s - 6.
A rectangle measures 3 cm by 5 cm. Find the corresponding measurements of the image of the rectangle after an enlargement of scale factor:
(a) - 0.75
(b) -1.5
(c) -3

1m 53s - 7.
The radius of a circle is 3.5 cm. Find the circumference of its image after an enlargement of scale factor 1.75.

1m 24s - 8.
A triangular field PQR is such that PQ = 20 m, PR = 30 m and QR = 40 m. The field is drawn to scale such that the side PQ is 3 cm long. Find the linear scale factor and the lengths of QR and PR.

3m 1s - 9.
The figure below shows a cone of base radius 28 cm and the slant side of length 35 cm. At a point P, 14 cm vertically below the vertex, the cone is cut across to form a smaller one. Calculate the base radius of the smaller cone.

3m 4s - 10.
A floor in a plan of a house measures 20 cm by 13 cm. Find the area of the actual house if the linear scale factor is 50.

1m 53s - 11.
The corresponding lengths of two similar photographs are 12 cm and 30 cm. The area of the larger photograph is 750 #cm^2#. Find the:
(a) area scale factor.
(b) area of the smaller photograph.

1m 44s - 12.
The floor of a room measuring 15 m by 9 m requires 3 375 square tiles. Find the measurements of each tile. If the tiles available were twice as long, determine the number of tiles that would be required.

3m 38s - 13.
The ratio of the area of two similar rooms is #4/25#
(a) Find the area of the bigger room if the area of the smaller room is 8#m^2#.
(b) Find the ratio of their lengths.
(c) If the length of the larger room is 10 m, find the length of the smaller one.

1m 44s - 14.
The corresponding sides of two similar regular pentagons are 3 cm and 7 cm respectively.
(a) Find the ratio of their areas.
(b) Calculate the area of the larger if the area of the smaller is 36 #cm^2#.

1m 28s - 15.
Mwangi has two balloons, one yellow and the other green. The radius of the yellow balloon is 7 cm while that of the green balloon is 21 cm. Find the ratio of their surface areas.

1m 6s - 16.
(a) In the figure below, name three pairs of
(i) Corresponding sides.
(ii) Corresponding angles.
(b) What can you say about triangles AOB and COD?

2m 22s - 17.
In the figure below, triangle ABE is similar to triangle ACD. Calculate the length of BC.

1m 47s - 18.
In the figure below, SR is parallel to PQ. Calculate the lengths of SR and PX.

2m 53s - 19.
In the figure below, #angle# EHG = #angle# EFH = 90°, HF = 5 cm and EF = 12 cm. Calculate the length HG and FG.

4m 35s - 20.
A triangle KLM is similar to a triangle PQR. KL = 5 cm, LM = 4 cm and #angle# KLM = 46°. Construct triangle PQR such that QR = 6 cm.

6m 22s - 21.
ABCD and PQRS are similar rectangles. AB = 3 cm and BC = 7 cm. If PQ = 5 cm, construct rectangle PQRS.

6m 9s - 22.
WXYZ is a rectangle in which WX = 8 cm and XY = 6 cm. F is a point on YZ such that YF = 6 cm. Construct a rectangle YEFG similar to WXYZ such that YF is the diagonal.

7m 24s - 23.
In the figure below, #angle# TQS = #angle# QPR, PR//TS, PQ = 15 cm, QR = 6 cm and ST = 8 cm. Calculate QT.

2m 31s - 24.
The vertices of an object and its image after an enlargement are A(0, 0), B (1, 1), C (2, 0), D(1, -1) and A'(3, 3), B'(5, 5), C'(7, 3), D'(5, 1) respectively. Find the centre and scale factor of the enlargement.

8m 48s - 25.
Given that P (3, 4), Q(4, 4), R(6, 4), S (7, 1) and T (5, 0) are the vertices of an object, find the vertices of the image after an enlargement with the centre at (0, 0) and scale factor #1/2#

8m 38s