Question

ln ∆ PQR, LPQR =90°. find the length of the hypotenuse PR if PQ2+ QR2= 144​

Answer 1

Please refer the attachment to view the diagram.

It is given that:

➡ In the ∆PQR, ∠PQR measures 90°.

➡ Side PQ² + QR² = 144

We need to find the length of the hypotenuse.

Solution:

The main concept theorem to be applied in this question is the Pythagoras theorem applicable to right angled triangles.

Formula:

$\sf{\implies\:Alitutde^2+Base^2=Hypotenuse^2}$

Here,

➡ Altitude = PQ

➡ Base = QR

➡ Hypotenuse = PR

Applying the same formula here:

$\sf{\longrightarrow\:PQ^2+QR^2=PR^2}$

We know that:

$\sf{\longrightarrow\:PQ^2+QR^2=144}$

Now, combining the following equations:

$\sf{\longrightarrow\:PR^2=144\:cm}$

$\sf{\longrightarrow\:PR=\sqrt{144}}$

$\sf{\longrightarrow\:PR=12\:cm}$

The length of the hypotenuse "PR" is 12 cm.

Pythagoras Theorem:

According to the Pythagoras theorem, the sum of the squares of the altitude and the base of a right angled triangle is equal to the square of its hypotenuse. So to find the length of the hypotenuse, we need to find the square root of the sum of the altitude and base measures.