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
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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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