If a quantity is multiplied by a number then the number is called scale factor. In scaling, It is used as a multiplier. It is also called as representative ratio.
For example, Rectangles ABCD and EFGH are similar. Length and breadth of a rectangle ABCD are 3 and 2. Length and breadth of rectangle EFGH are 9 and 6. Here length of rectangle EFGH is 3 times the length of rectangle ABCD. Breadth of rectangle EFGH is 3 times the breadth of rectangle ABCD. So, 3 is the scale factor for rectangle ABCD.
LEFGH = 3 x LABCD L and B stands for length and breadth
BEFGH = 3 x BABCD
Similarly, 1/3 is the scale factor for rectangle EFGH.
LABCD = 1/3 x LEFGH
BABCD = 1/3 x BEFGH
Examples of Scale Factor
1) 10 is the result of multiplying 5 by 2 . Here 2 is the scale factor for 5.
2) If there are two similar polygons, the side of one polygon is formed by multiplying the side of other
polygon by 19.Then 19 is the scale factor.
3) If the ratio of corresponding sides of two similar triangles is 12.Then scale factor is 12.
Solved Problems of Scale Factor
1) If side of a square ABCD is 5m. Find the side of square PQRS if scale factor
is 11.
Solution:
Let S be the side of square
SABCD = 5cm
Scale factor = 11
SPQRS = 11 x SABCD
= 11 x 5
= 55cm
2) What is the image of R(7,8) under dilation with center(0,0) for scale
factor of 10?
Solution:
R = (7, 8)
Scale factor = 10
Image = (7 x 10, 8 x 10)
Image = (70, 80)
3) Point S (0, -39) is dilated to T with center (0, 0) for scale factor of 1/13.
What are the coordinates of T?
Solution:
S = (0, -39)
Scale factor = 1/13
T = (0 x 1/13, -39 x 1/13)
= (0, -39/13)
T = (0, -3)
4) Find the representative ratio for a given scale of 3m = 15km.
Solution:
Convert kilometers into meters.
1 km = 1000m.
15km = 15 x 1000m
15km = 15000m
Representative ratio = 3m/15km
= 3m/ 15000m
= 1/5000
Representative ratio= 1: 5000
4) ABC and PQR are two similar triangles. Length of sides of triangle ABC are
AB = 3, BC = 4, CA = 17 and lengths of triangle PQR are PQ = 7, QR = 28/3.
Find RP.
Solution:
Given that ABC and PQR are similar triangles.
Therefore corresponding sides are equal
So, AB/PQ = BC/QR = CA/RP
3/7 = 4/(28/3) = 17/RP
3/7 = (4 x 3)/28 = 17/RP
3/7 = 12/28 = 17/RP
3/7 = 3/7 = 17/RP
So here scale factor is 3/7
3/7 = 17/RP multiply both sides by 7RP
7RP (3/7) = 7RP (17/RP)
3RP = 7 x 17
3RP = 119 divide both sides by 3
3RP/3 = 119/3
RP = 119/3
Related Tags
Representation: Ratio Or Scale Factor, Ratio Or Scale Factor (Representation), Help on Representation of Ratio Or Scale Factor