Ahaan's rectangle

Geometry Level 2

In rectangle $ABCD$ , $AD = 15$ and point $E$ is on side $BC$ such that $EA = 13$ and $ED = 14$ . What is the area of rectangle $ABCD$ ?

This problem is shared by Ahaan Rungta .

The answer is 168.

1 solution

Arron Kau Staff
May 13, 2014

Observe that the area of the rectangle is double the area of the triangle $\triangle EAD$ , because the rectangle and triangle have both common base and height. By Heron's Formula, the area of triangle $\triangle EAD$ is

$\sqrt{ (21) (21-13) (21-14) (21-15) } = 84.$

Therefore, the area of the rectangle is $2 \cdot 84 = 168$ .

Use cosine rule to find angle EDA which gives 37 degree(famous angle in physics!).which gives angle EDC=63 degree so DC=14cos63=56/5 Area=56/5*15=168 Ans. Sorry for not formatting.

Pranjal Shukla - 6 years, 11 months ago

Ahaan's rectangle

The answer is 168.

1 solution

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