Question

The length of the hypotenuse PR of an isosceles right angled triangle PQR, where PQ is 4 cm, is......... *

Answer 1

Answer:

$4 \sqrt{2}$

Step-by-step explanation:

If PQR is an isosceles Right angled Triangle then PQ=PR.

PQ=PR=4cm.

According to pythagoras theorem,

PR²=PQ²+QR²

PR²=4² + 4²

PR²= 16 + 16

PR²= 32

PR= 4√2

Answer 2

Given:

Isosceles right-angled triangle PQR

Length of PQ = 4cm

To find:

Length of the hypotenuse PR.

Solution:

In a right-angle triangle, the hypotenuse is the longest side. Since this triangle is an isosceles triangle, its two sides are equal. The two sides are PQ and QR.

The length of PQ is given as 4cm. Then, the length of QR is also 4cm.

$PQ=QR=4cm$

According to the Pythagoras theorem, in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides of the triangle.

$PR^{2} =PQ^{2} +QR^{2}$

$PR^{2} =4^{2} +4^{2}$

$PR^{2} =16+16$

$PR^{2} =2*16$

Taking square root on both sides,

$PR=\sqrt{2*16}$

$PR=4\sqrt{2} cm$

Hence, the length of the hypotenuse PR of the isosceles right-angled triangle PQR is $4\sqrt{2} cm$.

The length of the hypotenuse PR of the isosceles right-angled triangle PQR is $4\sqrt{2} cm$.