IIMB 2001 (QA) PYQs

In $\triangle A B C, A B=16 \mathrm{~cm}, A C=12 \mathrm{~cm}$ and $B C=21 \mathrm{~cm}$ then find the length of angle bisector $A D$ (in cm)?

In the given diagram $\triangle ABC$ is a right-angled triangle, $\angle ABC=90\degree$ , $BD ⊥ AC$. If $AB:AC=3:5$ and area of $\triangle ABD$ is $90$ cm$^2$, then the area of $\triangle ABC$(in cm$^2$) is

In $\triangle A B C, D$ and $E$ are points on the sides $A B$ and $A C$, respectively, such that $D E||$ $B C$. If $\mathrm{AD}=5 \mathrm{~cm}, \mathrm{DB}=9 \mathrm{~cm}, \mathrm{AE}=4 \mathrm{~cm}$ and $B C=15.4 \mathrm{~cm}$, then the sum of the lengths of $D E$ and $E C$ (in cm ) is: