Math, asked by chimaji1674, 10 months ago

Heights of two similar triangles are 4cm and 12cm find there ratio of area​

Answers

Answered by jangidsagar945
0

Answer:

Let us also draw perpendiculars

A

P

and

D

Q

from

A

and

D

respectively on to

B

C

and

E

F

as shown.

enter image source here

It is apparent that

Δ

A

P

B

and

Δ

D

E

Q

are also similar as all respective angles are equal. Hence,

A

B

D

E

=

A

P

D

Q

=

B

P

E

Q

We also have

Δ

A

B

C

=

1

2

×

B

C

×

A

P

and

Δ

D

E

F

=

1

2

×

E

F

×

D

Q

and

Δ

A

P

B

Δ

D

E

Q

=

B

C

×

A

P

E

F

×

D

Q

=

B

C

E

F

×

A

P

D

Q

But

A

P

D

Q

=

A

B

D

E

=

B

C

E

F

and hence

Δ

A

P

B

Δ

D

E

Q

=

B

C

E

F

×

B

C

E

F

=

B

C

2

E

F

2

and as

B

C

E

F

=

A

C

D

F

=

A

B

D

E

Δ

A

P

B

Δ

D

E

Q

=

A

C

2

D

F

2

=

B

C

2

E

F

2

=

A

B

2

D

E

2

Hence if sides of two similar triangles are in the ratio

a

:

b

, their areas are in the proportion

a

2

:

b

2

As in given case sides are in the ratio of

4

:

9

.

ratio of their areas is

4

2

:

9

2

or

16

:

81

.

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