Dr. Sanjeev Verma and R.K. Tyagi Solutions for Chapter: Properties of Triangles, Exercise 4: ASSIGNMENT 7.4

The perpendicular length of a right triangle, whose hypotenuse is $15 \mathrm{cm}$ and base is $12 \mathrm{cm}$, is

If $a, b, c$ are the three positive integers, then which of the following is true for Pythagorean triplets?

The sides of a triangle are given below. Determine if it is a right triangle:

$a=6 \mathrm{cm}, b=8 \mathrm{cm}, c=10 \mathrm{cm}$

The sides of a triangle are given below. Determine if it is a right triangle:

$a=5 \mathrm{cm}, b=8 \mathrm{cm}, c=11 \mathrm{cm}$

Angles $B$ and $C$ of a $∆ABC$ are $30°$ and $60°$ respectively. Then, $A{B}^2+A{C}^2=B{C}^2$.

Angles $B$ and $C$ of a $∆ABC$ are $30°$ and $60°$ respectively. Then, $A{B}^2+B{C}^2=A{C}^2$

Angles $B$ and $C$ of a $∆ABC$ are $30°$ and $60°$ respectively. State which of the following is/are 'True'.

$A{C}^2+B{C}^2=A{B}^2$

$ABC$ is an isosceles triangle right-angled at $C$. Prove that $A{B}^2=2A{C}^2$.