Question

Given : ∆ACD ~ ∆ ABE
find ar(ABE)/ar(ACD)​

Answer 1

Answer:

1/2

Step-by-step explanation:

In right triangle ABC

by using Pythagoras theorem

AB²+BC²=AC²

AB²+AB²=AC² (as AC=BC)

2AB²=AC² {say (i)}

✓2 AB=AC

since ∆ACD ~ ∆ABE

ar(ABE)/ar(ACD) = AB²/AC²

= AB²/2AB² {From (i)}

=1/2

Above we used this theorem

Theorem : If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.