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.

Explanation:

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

`D=√((x-a)^2+(y-b)^2+(z-c)^2)`

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

Then,

`|PQ|=√((6-4)^2+(6-4)^2+(1-2)^2)=√(2^2+2^2+(-1)^2)\\\\=√(4+4+1)=√(9)=3`

`|QR|=√((4-4)^2+(10-4)^2+(5-2)^2)=√(0+6^2+3^2)\\\\=√(36+9)=√(45)=3√(5)`

`|RP|=√((6-4)^2+(6-10)^2+(1-5)^2)=√(2^2+(-4)^2+(-4)^2)\\\\=√(4+16+16)=√(36)=6`

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