Question

Q1. If a triangle having sides 50 cm., 14 cm, and 48 cm., then state wheather given triangle is right angled triangle or not.​

Answer 1

Explanation:

Answer :

Here, It is stated that the triangle having sides 50 cm., 14 cm, and 48 cm. So, we have to prove that whether the given triangle is right angled triangle or not.

For That :

We will be using the Pythagoras Theorem

Given Sides :-

• Side - A → 50 cm
• Side - B → 48 cm
• Side - C → 14 cm

According to the Pythagoras Theorem , the sum of the square of Base side and perpendicular side is equal to the square of the longest side i.e, hypotenuse.

Pythagoras Theorem :

⠀⠀⠀⠀⠀⠀

$\begin{gathered}{\bullet \: {\boxed{\sf {AC^{2} = AB^{2} + BC^{2}}}}} \\ \\ \end{gathered} </p><p>∙$

So, here the longest side is Side A of measurement 50 cm.

So, Now

Applying Pythagoras Theorem in it, we get :

The three sides , so let's plug the values in the formula :-

$\begin{gathered}\dashrightarrow\:\:\sf AC^{2} = AB^{2} + BC^{2}\\ \\\end{gathered} </p><p>$

$\begin{gathered}\dashrightarrow\:\:\sf 50^{2} = 48^{2} + 14^{2}\\ \\\end{gathered} </p><p>$

$\begin{gathered}\dashrightarrow\:\:\sf 2500 = 2304 + 14^{2} \\ \\\end{gathered} </p><p>$

$\begin{gathered}\dashrightarrow\:\:\sf 2500 = 2304 + 196 \\ \\\end{gathered}$

$\begin{gathered}\dashrightarrow\:\:\sf 2500 = 2500 \\ \\\end{gathered} </p><p>$

If in a triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle. It is stated as the converse of the Pythagoras Theorem.