$A D$ is a median of triangle $A B C$ and area of $\triangle A D C=15 cm^2$, then ar $(\triangle A B C)$ is
A$15 cm^2$
B$22.5 cm^2$
C$30 cm^2$
D$37.5 cm^2$
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C$30 cm^2$
(c) $30 cm^2$ A median of a triangle divides it into two triangles of equal area. Therefore, $\operatorname{ar}(\triangle A B C)=2 \operatorname{ar}(\triangle A D C)=2 \times 15 cm^2=30 cm^2$
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Each side of a triangle is multiplied with the sum of the squares of the other two sides. If the sum of all such possible results is 6 times the product of the sides, then the triangle must be