Question

Given that triangle ABC and DEC are right triangles such that 3DE=2AB. What is the ratio of areas of triangles ABC and DEC? A. 2/3 B. 3/2 C. 4/9 D. Not possible

Answer 1

`9:4`.

Explanation:

We have, in `DeltaBAC` and `DeltaDEC`,

`/_BAC=/_DEC, and, /_ACB=/_ECD`.

Hence, `DeltaBAC` and `DeltaDEC` are similar.

Let us denote by `[DeltaBAC]` the Area of `DeltaBAC`.

It is known from Geometry, that,

`[DeltaBAC] : [DeltaDEC]=BA^2 : DE^2...............(ast)`.

Given `3DE=2AB rArr (BA)/(DE)=3/2`.

`:. (ast) rArr [DeltaBAC] : [DeltaDEC]=9:4`.