Math, asked by deepsikhadandapat9, 1 day ago

(DJ ZJILI (a) 2213 cm 10. The area of incircle of an equilateral triangle is 154 cm². The perimeter of the triangle is (a) 71.5 cm (b) 71.7 cm (c) 72.3 cm (d) 72.7 cm dins is​

Answers

Answered by nihasrajgone2005
0

Answer:

Given Area of circle=154cm

2

⇒πr

2

=154cm

2

⇒r

2

=

22

154×7

=49cm

⇒r=

49

=7cm

ABC is an equilateral △, h is the altitude of △ABC

0 is the incenter of △ABC, and this is the point of intersection of the angular bisectors. Hence, these bisectors are also the altitude and medians whose point of intersection divides the medians in the ratio 2:1

∴∠ADB=90° & OD=

3

1

AD & OD is radius of circle. Then,

r=

3

h

⇒h=3r=3×7=21cm

Let each side of an equilateral triangle be 'a', then altitude of an equilateral triangle is (

2

3

) times its side. So that

h=

2

3

a⇒a=

3

2h

=

3

2×21

=

3

2×21

3

=14

3

cm

Perimeter of triangle ABC=3a=3×14

3

cm=42

3

cm=42×1.73

=72.66cm

2

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Step-by-step explanation:

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Answered by llSingleKingll
6

Step-by-step explanation:

Given Area of circle=154cm

2

⇒πr

2

=154cm

2

⇒r

2

=

22

154×7

=49cm

⇒r=

49

=7cm

ABC is an equilateral △, h is the altitude of △ABC

0 is the incenter of △ABC, and this is the point of intersection of the angular bisectors. Hence, these bisectors are also the altitude and medians whose point of intersection divides the medians in the ratio 2:1

∴∠ADB=90° & OD=

3

1

AD & OD is radius of circle. Then,

r=

3

h

⇒h=3r=3×7=21cm

Let each side of an equilateral triangle be 'a', then altitude of an equilateral triangle is (

2

3

) times its side. So that

h=

2

3

a⇒a=

3

2h

=

3

2×21

=

3

2×21

3

=14

3

cm

Perimeter of triangle ABC=3a=3×14

3

cm=42

3

cm=42×1.73

=72.66cm

2

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