Question

In a triangle PQR right angled at Q, PQ = 24cm, QR = 10 cm , find PR.

Answer 1

Answer:

It is given in the question that PQR is a right-angled triangle and it is right-angled at P.

So, we can apply the Pythagoras theorem here.

If it is right-angled at P then the side opposite to P will be the hypotenuse of the triangle i.e. QR and the other sides are given as PQ = 10 cm and PR = 24 cm.

Now, by applying the Pythagoras theorem i.e. in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides, we can find QR.

Given, PQ = 10 cm, PR = 24 cm and QR =?

By applying Pythagoras theorem in triangle PQR, we get (Hypotenuse)2 = (Perpendicular)2 + (Base)2

(QR)2 = (PQ)2 + (PR)2

(QR)2 = (10)2 + (24)2

(QR)2 = 100 + 576

(QR)2 = 676

QR = 26 cm

Thus, QR is equal to 26 cm.

Answer 2

Given: In a triangle PQR right-angled at Q, $PQ = 24cm, QR = 10cm.$

We have to find the value of PR.

By using the Pythagorean theorem, we are solving the above problem.

As we know that the Pythagorean theorem states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

We are solving in the following way:

We have,

$PQ = 24cm, QR = 10cm.$

From the given statement, we can write:

$=>PR^{2} =PQ^{2} +QR^{2} \\=>PR^{2}=24^{2} +10^{2} \\=>PR^{2}=576+100\\=>PR^{2}=676$

Solving the above equation further we get,

$=>PR=\sqrt{676} \\=>PR=26cm.$

Hence, the value of$PR$ is$26cm.$