Scale factor and similarity
Maps and Models are made on a scale. Measure the distance between any two cities marked in
the map and compare it with the actual distance between two cities to get the ratio between the two
distances. The scale is written as a ratio. The ratio is already on marked on every map and is known as scale
factor.
Similar figure: the ratio of two corresponding sides in similar figures is called the scale factor.
Scale factor= ℎ
ℎ
If one shape can become another using resizing then the shapes are similar.
Hence, two shapes are similar when one can become the other after a resize, flip, side or turn.
(i) A model of a garden is made on the scale of 1:100. The length of model garden is 80cm. what is
the actual length of garden?
(a) 8000cm (b) 800cm (c) 8m (d) 800m
(ii) The breadth of garden is 60m, then breadth of the model garden is:
(a) 6cm (b) 6m (c) 60cm (d) 30cm
(iii) What are the common elements in two similar triangles?
(a) All corresponding sides are equal (c) ratio of corresponding sides are equal
(b) All corresponding angles are equal (d) both (b) and (c)
(iv) Which of the following is not a criteria for similar triangles
(a) SSA (b) AAA (c) SAS (d) SSS
(v) Actual Area of the garden is
(a) 480m² (b) 4800m² (c) 4800cm² (d) 48m²
Answers
Given : (i) A model of a garden is made on the scale of 1:100. The length of model garden is 80cm.
The breadth of garden is 60m
To Find : what is the actual length of garden
(a) 8000cm (b) 800cm (c) 8m (d) 800m
breadth of the model garden
(a) 6cm (b) 6m (c) 60cm (d) 30cm
common elements in two similar triangles
(a) All corresponding sides are equal (c) ratio of corresponding sides are equal (b) All corresponding angles are equal (d) both (b) and (c)
Which of the following is not a criteria for similar triangles
a) SSA (b) AAA (c) SAS (d) SSS
Actual Area of the garden is
(a) 480m² (b) 4800m² (c) 4800cm² (d) 48m²
Solution :
model of a garden is made on the scale of 1:100
The length of model garden is 80cm.
=> actual length of garden = 100 x 80 = 8000 cm
The breadth of garden is 60m = 60 x 100 = 6000 cm
breadth of the model garden = 6000/100 = 60 cm
common elements in two similar triangles
(c) ratio of corresponding sides are equal
(b) All corresponding angles are equal
(d) both (b) and (c)
a) SSA is not a criteria for similar triangles
Actual Area of the garden is 60 x 80 = 4800 cm²
Learn More:
There are two different maps of Ohio. The scale on the first map is 1 ...
https://brainly.in/question/23176420
On a map scale, 2 inches represents 60 miles. Which graph best ...
https://brainly.in/question/17418843
A scale used on a map is 1:900,000. If the distance on the map ...
https://brainly.in/question/17096716