Question

Triangle P Q R is shown. Angle Q P R is a right angle. The length of Q P is 8 StartRoot 3 EndRoot and the length of P R is 8. Consider triangle PQR. What is the length of side QR? 8 units 8 StartRoot 3 EndRoot units 16 units 16 StartRoot 3 EndRoot units

Answer 1

Answer:

Length of side QR is 16 units.

Step-by-step explanation:

Given that dimensions of $\triangle PQR$ are as follows:

$\angle QPR =90^\circ$

Side QP $= 8 \sqrt3\ units$

Side PR = 8 units

To find, side QR = ? units

Please refer to the attached figure for the representation of the given dimensions.

Base is side QP,

Perpendicular is side PR and

Hypotenuse is side QR.

In a right angled triangle, Pythagorean theorem holds true i.e.

Accoring to pythagoras theorem:

$\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}$

$\Rightarrow QR^{2} = QP^{2} + PR^{2}$

Putting the values of QP and PR:

$\Rightarrow QR^{2} = (8\sqrt3)^{2} + 8^{2}\\\Rightarrow QR^{2} = 64 \times 3+ 64\\\Rightarrow QR^{2} = 64 \times 4\\\Rightarrow QR = 8 \times 2\\\Rightarrow QR = 16\ units$

So, the value of length of side QR is 16 units.