M L Aggarwal Solutions for Chapter: Triangles, Exercise 9: Chapter Test

In the adjoining figure, $ABCD$ is a trapezium in which $AB\parallel DC$. If $2AB=3DC,$find the ratio of the areas of $△AOB$ and $△COD$.

In the adjoining figure, $AB\parallel DC.$ If $\angle A=90°, DC=7cm, AB=17 cm$ and $AC=25 cm$, find the length of $BC.$

In the adjoining figure , find the length of $AD$ in terms of $b$ and $c.$

In the adjoining figure, $\angle D=90°$. If $AB=16 \mathrm{cm}, BC=12 \mathrm{cm}$ and $CA=6 \mathrm{cm}$, find the length of $CD.$

In the adjoining figure, $\angle B=90°$. If $AE=DC=13 cm, BE=5 cm$ and $AE=EC=x cm,$ find the length of $AB$ and the value of $x.$ 

In the adjoining figure , $△ABC$ is right angled at $C ; P$ and $Q$ are points on the sides $CA$ and $CB$ respectively which divide these sides in the ratio $2 : 1$. Prove that $9 A{Q}^2=9A{C}^2+4B{C}^2$

In the adjoining figure , $△ABC$ is right angled at $C ; P$ and $Q$ are points on the sides $CA$ and $CB$ respectively which divide these sides in the ratio $2 : 1$. Prove that $9 B{P}^2=9B{C}^2+4A{C}^2$

In the adjoining figure , $△ABC$ is right angled at $C ; P$ and $Q$ are points on the sides $CA$ and $CB$ respectively which divide these sides in the ratio $2 : 1$. Prove that $9 \left(A{Q}^2+B{P}^2\right)=13 A{B}^2$