Math, asked by rajvermalkr07, 3 months ago

ig.
Find the area of the following figures.
D
F
E
7 cm
2 cm
2.4 cm
A
B
C С
8 cm
(a)​

Answers

Answered by rammarammma
1

Answer:

(i) If AD = 3.6 cm, AB = 10 cm and AE = 4.5 cm, find EC and AC.

(ii) If AB = 13.3 cm, AC = 11.9 cm and EC = 5.1 cm, find AD.

(iii) If

AD

DB

=

4

7

and AC=6.6 cm, find AE.

(iv) If

AD

AB

=

8

15

and EC=3.5 cm, find AE.

ANSWER:

(i)

In △ ABC, it is given that DE∥BC.

Applying Thales' theorem, we get:

AD

DB

=

AE

EC

∵ AD = 3.6 cm , AB = 10 cm, AE = 4.5 cm

∴ DB = 10 - 3.6 = 6.4 cm

or,

3.6

6.4

=

4.5

EC

or, EC =

6.4×4.5

3.6

or, EC =8 cmThus, AC = AE +EC = 4.5 + 8 = 12.5 cm

(ii)

In △ABC, it is given that DE ∥BC.Applying Thales' Theorem, we get:

AD

DB

=

AE

EC

Adding 1 to both sides, we get:

AD

DB

+1 =

AE

EC

+1⇒

AB

DB

=

AC

EC

13.3

DB

=

11.9

5.1

⇒DB =

13.3×5.1

11.9

= 5.7 cm

Therefore, AD = AB - DB = 13.5 - 5.7 = 7.6 cm

(iii)

In △ABC, it is given that DE∥BC.Applying Thales' theorem, we get:

AD

DB

=

AE

EC

4

7

=

AE

EC

Adding 1 to both the sides, we get:

11

7

=

AC

EC

⇒EC =

6.6×7

11

= 4.2 cmTherefore, AE = AC -EC= 6.6-4.2 = 2.4 cm

(iv)

In △ABC, it is given that DE∥BC.Applying Thales' theorem, we get:

AD

AB

=

AE

AC

8

15

=

AE

AE + EC

8

15

=

AE

AE + 3.5

⇒8AE + 28 = 15AE⇒7AE = 28⇒AE = 4 cm

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