Question

In a right triangle PQR, ∠Q=90°. If PQ=20 cm and QR= 21 cm, then find the length of the side PR.

Answer 1

The length of PR is 17 cm

Step-by-step explanation:

We are given that in a right angle triangle pqr angle Q is equal to 90 degree

So, PQ = Perpendicular

QR= Base

PR = Hypotenuse

PQ=15 cm

QR = 8 cm

To find the length of Hypotenuse We will use Pythagoras theorem

\begin{gathered}Hypotenuse^2=Perpendicular^2+Base^2\\PR^2=PQ^2+QR^2\\PR=\sqrt{15^2+8^2}\\PR=17\end{gathered}

Hypotenuse

2

=Perpendicular

2

+Base

2

PR

2

=PQ

2

+QR

2

PR=

15

2

+8

2

PR=17

Hence The length of PR is 17 cm

Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

In a right triangle PQR, ∠Q = 90°. If PQ = 20 cm & QR = 21 cm .

$\underline{\bf{Explanation\::}}$

Firstly, attachment a figure of right angled triangle as according to the question.

A/q

$\underline{\mathcal{USING\:FORMULA\:OF\:PYTHAGORAS\:THEOREM\::}}$

$\mapsto\tt{(Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}}$

$\mapsto\tt{(PR)^{2} = (PQ)^{2} + (QR)^{2}}$

$\mapsto\tt{(PR)^{2} = (20)^{2} + (21)^{2}}$

$\mapsto\tt{(PR)^{2} = 400 + 441}$

$\mapsto\tt{(PR)^{2} =841}$

$\mapsto\tt{PR =\sqrt{841} }$

$\mapsto\bf{PR =29\:cm}$

Thus;

The length of the side of PR will be 29 cm .