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Consider triangle PQR. What is the length of side QR?
A. 8 units
B. 8/3 units
C. 16 units
D. 16/3 units

Consider triangle PQR What is the length of side QR A 8 units B 83 units C 16 units D 163 units class=

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ANSWER

C) 16

EXPLANATION

Using the Pythagoras Theorem, we obtain:

QR² =PR²+ PQ²

From the diagram,

[tex]PQ = 8 \sqrt{3} [/tex]

[tex]PR=8[/tex]

We substitute into the formula to get;

[tex]|QR| ^{2} = {8}^{2} + {(8 \sqrt{3} )}^{2} [/tex]

[tex]|QR| ^{2} = 64+ 192[/tex]

[tex]|QR| ^{2} = 256[/tex]

Take square root

[tex]|QR| = \sqrt{256} [/tex]

[tex]|QR| = 16[/tex]

Answer:

The length of side QR is 16 units.

Option C is correct.

Step-by-step explanation:

Given a right angled triangle QPR in which length of sides are

[tex]PQ=8\sqrt3 units[/tex]

[tex]PR=8 units[/tex]

we have to find the length of side QR

As QPR is right angled triangle therefore we apply Pythagoras theorem

[tex](hypotenuse)^2=(Base)^2+(Perpendicular)^2[/tex]

[tex]QR^2=PQ^2+PR^2[/tex]

[tex]QR^2=(8\sqrt3)^2+8^2[/tex]

[tex]QR^2=192+64=256[/tex]

Take square root on both sides

[tex]QR=16 units[/tex]

Hence, the length of side QR is 16 units.

Option C is correct.

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