Question

In triangle PQR, if angel QPR-90degree.Then PRsquare=?

Answer 1

$\textbf {Theory}$ :

This question can be solved by using Pythagoras Theorem. If you are not familiar with Pythagoras Theorem, let me tell you what is it first.

$\textbf {Pythagoras Theorem}$ :

The Pythagoras Theorem states that in a right angled triangle, the square of the hypotenuse which is the longest side of the triangle is always equal to the sum of the square of the other two sides, that is, altitude and base respectively.

Lets consider that a certain triangle has hypotenuse h units, and base and altitude a and b units respectively. Then, by Pythagoras Theorem,

h² = a² + b²

$\textbf {Solution}$ :

Now that we know what Pythagoras Theorem is, let's return to the problem.

Keep a look that the side opposite to the right angle is the hypotenuse. Thus is because 90° is the largest angle in a right angled triangle and thus the side opposite to it will be the longest.

So, we are provided with a Δ PQR such that <P = 90°. Thus, we know that QR is the hypotenuse of this triangle.

PR and PQ are the other two sides.

Applying Pythagoras Theorem to Δ PQR,

h² = a² + b²

QR² = PR² + PQ²

PR² = QR² - PQ²

$\textbf {Answer}$ :

This is a question regarding evaluations and doesn't deal with values / magnitudes. Thus, your final answer is (QR² + PQ²).

Answer 2

In a right ∠d Δ PQR note the following things :

The longest side is called the hypotenuse.

By Pythagoras Theorem :

( Hypotenuse )² = ( height )² + ( base )²

Well height and base matters on the angle chosen.

The opposite side of the angle chosen is called the height .

The side which is neither the base nor the height is hence the base..

Given is a triangle of PQR.

We have to find the value of PR²

QR is the opposite side to the right angle.

By property of triangle :

The largest angle has largest side opposite to it.

Hence QR is the largest side and its the hypotenuse !

Applying Pythagoras theorem :

QR² = PQ² + PR²

==> PR² = QR² - PR²

ANSWER :-

PR² = QR² - PR²

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