Math, asked by siddhantgupta928, 7 months ago

a trapezium is made up of triangles triangles ABE and BCE right angled triangle. Triangle CDE and BCE isosceles triangles (BC=BE) AE = 3cm and EB=4cm​

Answers

Answered by sreelureddylakshmi1
2

Answer:

Step-by-step explanation:

It is given that ΔABC is an isosceles triangle right angled at B, so,

AB=BC

In ΔABC, by Pythagoras theorem,

AC  

2

=AB  

2

+BC  

2

 

AC  

2

=AB  

2

+AB  

2

 

AC  

2

=2AB  

2

 

As ΔABE∼ΔACD is given, then it is known that the ratio of areas of equilateral triangles is equal to the ratio of the squares of their corresponding sides, so,

ar(ΔACD)

ar(ΔABE)

​  

=  

AC  

2

 

AB  

2

 

​  

 

ar(ΔACD)

ar(ΔABE)

​  

=  

2AB  

2

 

AB  

2

 

​  

 

ar(ΔACD)

ar(ΔABE)

​  

=  

2

1

​  

 

Therefore, ar(ΔABE):ar(ΔACD)=1:2

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