Question

Find the lengths of the sides of the triangle PQR. P(6, 6, 1), Q(4, 4, 2), R(4, 10, 5)|PQ| = |QR| = |RP| = $

Answer 1

Answer: |PQ| =3 units ,  |QR| = 3√5 units,  |RP| = 6 units.

Step-by-step explanation:

Distance between two points (a,b,c) and (x,y,z) is given by :-

$D=\sqrt{(x-a)^2+(y-b)^2+(z-c)^2}$

Given: P(6, 6, 1), Q(4, 4, 2), R(4, 10, 5)

Then,

$|PQ|=\sqrt{(6-4)^2+(6-4)^2+(1-2)^2}=\sqrt{2^2+2^2+(-1)^2}\\\\=\sqrt{4+4+1}=\sqrt{9}=3$

$|QR|=\sqrt{(4-4)^2+(10-4)^2+(5-2)^2}=\sqrt{0+6^2+3^2}\\\\=\sqrt{36+9}=\sqrt{45}=3\sqrt{5}$

$|RP|=\sqrt{(6-4)^2+(6-10)^2+(1-5)^2}=\sqrt{2^2+(-4)^2+(-4)^2}\\\\=\sqrt{4+16+16}=\sqrt{36}=6$

So, |PQ| =3 units ,  |QR| = 3√5 units,  |RP| = 6 units.