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In the following figure, the area of the isosceles right triangle ABE is 7 sq.cm. If EC=3BE, then the area of rectangle ABCD id (insq.cm.)

  1. 64
  2. 82
  3. 26
  4. 56
in Quantitative Aptitude 11.6k points 221 1489 2361 149 views

1 Answer

1 vote
Given: 1) $\text{Area of $\triangle$ ABC =7 cm$^{2}$}$

            2) $EC=3BE$

We know that area of triangle =$\frac{1}{2}*B*H$

so Area of $\triangle$ ABE $= \frac{1}{2}*B*H$

$\implies 7=\frac{1}{2}*B*H$

$\implies B*H=14 $

This can be also written as  $ \text{ BE*AB=14 cm $^{2}$}\cdots\cdots(i)$

Now area of rectangle $ABCD= AB*BC$

                               $\implies AB* (4*BE)$

                              $\implies 4*14=56 $ sq cm

 Note: $(BC=BE+EC\implies BE+3BE=4BE)$

Option $(D)$ is correct.
3.7k points 5 10 66

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