Question 132
Given the triangle $ABC$ right-angled at $A$, we construct on the hypotenuse the square $BCDE$ (with $D, E$ on the opposite side of $BC$ from $A$). Knowing that the areas of the triangles $ABE$ and $ACD$ are $6~\mathrm{m}^2$ and $27~\mathrm{m}^2$ respectively, what is the area of the triangle $ABC$?
(A) $3 \sqrt{2}~\mathrm{m}^2$
(B) $6~\mathrm{m}^2$
(C) $12~\mathrm{m}^2$
(D) $9 \sqrt{2}~\mathrm{m}^2$
(E) $18~\mathrm{m}^2$
(A) $3 \sqrt{2}~\mathrm{m}^2$
(B) $6~\mathrm{m}^2$
(C) $12~\mathrm{m}^2$
(D) $9 \sqrt{2}~\mathrm{m}^2$
(E) $18~\mathrm{m}^2$