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

Length of side QR is 16 units.

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 * 3+ 64\\\Rightarrow QR^(2) = 64 * 4\\\Rightarrow QR = 8 * 2\\\Rightarrow QR = 16\ units`

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