Question

the lenght of hypotenus PR of an isosceles right angled triangle PQR , where PQ is 4cm is_______.

Answer 1

Answer:

4√2 cm

Step-by-step explanation:

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Answer 2

Given,

An isosceles right-angled triangle PQR is right-angled at vertex Q.

Length of side PQ = 4 centimeters

To find,

Lenght of hypotenuse PR

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

As per the geometry of an isosceles right-angled triangle, the two sides of the triangle that contain the right angle, are equal in length.

So, in the isosceles right-angled triangle PQR right-angled at vertex Q, the sides PQ and QR are equal in length, i.e. PQ = QR = 4 cm.

So, on applying the Pythagoras theorem, we get:

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

=> (PR)^2 = (4)^2 + (4)^2

=> (PR)^2 = 32

=> PR = √32 = 4√2

Hence, the length of the hypotenuse PR of the isosceles right-angled triangle PQR is 4√2 centimeters.