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

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1 Answer
Jun 19, 2018

# 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#.