M L Aggarwal Solutions for Exercise 1: EXERCISE 12

Foot of a $10 \mathrm{m}$ long ladder leaning against a vertical wall is $6 \mathrm{m}$ away from the base of the wall. Find the height (in $\mathrm{m}$) of the point on the wall where the top of the ladder reaches.

In the above figure, $\angle B=90°$ and $\angle D=90°$. If $AB=12 \mathrm{cm}, AC=13 \mathrm{cm}, CE=10 \mathrm{cm}$ and $ED=6 \mathrm{cm}$, find the length of $BD$.

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, $ABC$ is a right-angled triangle at $C$. If $D$ is midpoint of $BC$, prove that $A{B}^2=4A{D}^2-3A{C}^2$.

In $△ABC, AB=AC=x \mathrm{cm}, BC=10 \mathrm{cm}$ and the area of $△ABC$ is $60 {\mathrm{cm}}^2$. Find $x$.

In a rhombus, if diagonals are $30 \mathrm{cm} \mathrm{and} 40 \mathrm{cm}$, find its perimeter (in $\mathrm{cm}$).

In the figure given below, $AB\left|\right|DC, BC=AD=13 \mathrm{cm}, AB=22 \mathrm{cm} \mathrm{and} DC=12 \mathrm{cm}.$ Calculate the height (in $\mathrm{cm}$) of the trapezium $ABCD$.

In the figure given below, $AB\parallel DC, \angle A=90°, DC=7 \mathrm{cm}, AB=17 \mathrm{cm} and AC=25 \mathrm{cm}.$ Calculate $BC$ (in $\mathrm{cm}$).