Find the lengths of the sides of the triangle PQR. P(0, 1, 5), Q(2, 3, 4), R(2, −3, 1) |PQ| = Correct: Your answer is correct. |QR| = Correct: Your answer is correct. |RP| = Correct: Your answer is correct. Is it a right triangle? Yes No Is it an isosceles triangle? Yes No

Answer:1. The values of |PQ|, |QR| and |RP| are 3, 3√5 and 6 respectively.2. No.3. No.Step-by-step explanation:The vertices of given triangle are P(0, 1, 5), Q(2, 3, 4), R(2, −3, 1).Distance formula:[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}[/tex]Using distance formula we get[tex]|PQ|=\sqrt{(2-0)^2+(3-1)^2+(4-5)^2}=\sqrt{9}=3[/tex][tex]|QR|=\sqrt{(2-2)^2+(-3-3)^2+(1-4)^2}=\sqrt{45}=3\sqrt{5}[/tex][tex]|RP|=\sqrt{(0-2)^2+(1-(-3))^2+(5-1)^2}=\sqrt{36}=6[/tex]The values of |PQ|, |QR| and |RP| are 3, 3√5 and 6 respectively.In a right angled triangle the sum of squares of two small sides is equal to the square of third side.[tex](3)^2+(3\sqrt{5})^2=54\neq 6^2[/tex]Therefore PQR is not a right angled triangle.In an isosceles triangle, the length of two sides are equal.The measure of all sides are different, therefore PQR is not an isosceles triangle.