Question

Case study Based -3
Similarity of Triangles
Ashok went to restaurant along with his friend shyam and he ordered one small pizza for him
and one bigger size pizza for his friends for a dinner party. Instead of eating this they are
comparing the slices of the pizza. And then a lot of questions came in to his mind.
Answer the following questions :-
16 em
20 cm
8 cm 10 cm
16 cm
(a) The slices of smaller pizza and bigger pizza are similar using?
(1) AA rule (II) SAS rule (III) SSS rule (IV)Slices are not similar
(b) The scale factor is
(1) 2 (1) 3 (1) 4(IV) I
(c) What will attect the similarity of any two polygons.
(1) They are flipped Horizontally
(II) They are dilated by a scale factor
(ID) They are translated down
(IVThey are not the mirror image of one another
dithe ratio of area of smaller slice two bigger slice is
12
1 1:8 ( 1 4
CIV 1:16
two similar triangle have a scale factor of a b which statement regarding the two
1​

Answer 1

Answer:

100

m = 100 \div 50m=100÷50

m = 2m=2

Answer 2

Answer:

a) SSS Rule b)2 c) They are not mirror image of one another d) 1:4

Step-by-step explanation:

Concept

• A simple closed curve or a polygon formed by three line-segments (sides) is called a triangle

Given

All side of big pizza and small pizza

Find

Right option of a, b , c and d question

Solution

a) 3rd option (SSS rule)

b) 1st option is right(2)

c) 4th option is right( They are not the mirror image of one another)

d) 2nd option is right 1:4

Step by step solution of (d) question

Area of isosceles triangle=$\frac{1}{2} [\sqrt{a^{2}-\frac{b^{2} }{4} } ]*b$

                                          $\frac{1}{2} [\sqrt16^{2} -\sqrt\frac{20^{2} }{4} ]*20\\=\frac{1}{2} [\sqrt{256} -\frac{400}{4} ]*20\\=\frac{1}{2} [\sqrt{156} ]*20\\=12.48*10\\=124.8$

Area of small isosceles triangle pizza=$\frac{1}{2} [\sqrt{a^{2}-\frac{b^{2} }{4} } ]*b$

                                                             $=\frac{1}{2}[\sqrt{8^{2} } -\sqrt{10^{2} }/4]*10\\=\frac{1}{2} [\sqrt{39} ]*10\\=31.2$

Ratio of big triangle:small triangle=124.8:31.2=1:4

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