O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 1: Exercise

$ABCD$ represents a quadrilateral in which $AD=13 \mathrm{cm}, DC=4 \mathrm{cm}, BC=3 \mathrm{cm}$, and $\angle ABD=\angle BCD=90°$. Find length of $AB$.

Three sides of a triangle are given below. Identify whether the triangle is right angled or not.

$4 \mathrm{cm}, 5 \mathrm{cm}, 6 \mathrm{cm}$

Three sides of a triangle are given below. Identify whether the triangle is right angled or not.

$1.2 \mathrm{cm}, 3.7 \mathrm{cm}, 3.5 \mathrm{cm}$

Three sides of a triangle are given below. Identify whether the triangle is right angled or not.

$4 \mathrm{cm}, 9.6 \mathrm{cm}, 10.4 \mathrm{cm}$

Three sides of a triangle are given below. Identify whether the triangle is right angled or not.

$2.2 \mathrm{cm}, 3.3 \mathrm{cm}, 4.4 \mathrm{cm}$

In the figure below all the distance in $\mathrm{cm}$, if the distance of $D$ from $A$ is $k \mathrm{cm}$, find the value of $k$. (correct up to two decimal places)

The sides of a right-angled triangle containing the right angle are $5x$ and $(3x-1) \mathrm{cm}$. If the area of the triangle be $60 {\mathrm{cm}}^2$, calculate the lengths of the sides of the triangle.

Given that$AB=BC=25 \mathrm{m}$. If $AE=7 \mathrm{m}$, and $CD=24 \mathrm{m}$, find the length of $DE$ and also show that triangle $ABE$ and triangle $BDC$ are congruent.