Math, asked by vihaanraisurana9, 1 day ago

if ab and cd are perpendicular find perimeter of triangle abc

Answers

Answered by thaniskanaidu
0

Answer:

Consider △ACD&△ABC

∠CAD=∠CAB

∠CDA=∠ACB

∴△ACD∼△ABC,{ By AA similarty criterion}

AB

AC

=

AC

AD

∴AC

2

=AB×AD−(1)

Similarily,△BCD∼△BAC{ by AA similarity criterion}

BA

BC

=

BC

BD

∴BC

2

=BA×BD−(2)

AC

2

BC

2

=

AB×AD

AB×BD

∴BC

2

×AD=AC

2

×BD

Answered by ananyanaskar28
0

Answer:

(i) From ΔABC and ΔDEC,

∠ABC=∠DEC=90  

 (Given)

and ∠ACB=∠DCE= Common

∴ ΔABC∼ΔDEC     (By A−A similarity)

(ii) In ΔABC and ΔDEC,

ΔABC∼ΔDEC       (proved in (i) part)

∴  

DE

AB

=  

CD

AC

 

Given: AB=6 cm,DE=4 cm,AC=15 cm,

∴  

4

6

=  

CD

15

 

⇒6×CD=15×4

⇒CD=  

6

60

 

⇒CD=10 cm.

(iii)  

Area of ΔDEC

Area of ΔABC

=  

DE  

2

 

AB  

2

 

          (∵ΔABC∼ΔDEC)

=  

(4)  

2

 

(6)  

2

 

=  

16

36

=  

4

9

 

∴ Area of ΔABC: Area of ΔDEC=9:4

Step-by-step explanation:

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