Question : In $\triangle X Y Z, P$ is a point on side YZ and XY = XZ. If $\angle X P Y=90°$ and $Y P=9\ \text{cm}$, then what is the length of $YZ$?

Option 1: 17 cm

Option 2: 18 cm

Option 3: 12 cm

Option 4: 15 cm

Question : Simplify the given expression. $\frac{x^3+y^3+z^3-3 x y z}{(x-y)^2+(y-z)^2+(z-x)^2}$

Option 1: $\frac{1}{3}(x+y+z)$

Option 2: $(x+y+z)$

Option 3: $\frac{1}{4}(x+y+z)$

Option 4: $\frac{1}{2}(x+y+z)$

Question : If $x(x+y+z)=20$, $y(x+y+z)=30$, and $z(x+y+z)=50$, then the value of $2(x+y+z)$ is:

Option 1: 20

Option 2: –10

Option 3: 15

Option 4: 18

Question : x, y, and z are 3 values, such that x + y = 12, y + z = 17 and z + x = 19. What is the average of x, y, and z?

Option 1: 10

Option 2: 8

Option 3: 6

Option 4: 4

Question : The lengths of the two sides of a triangle are 14 cm and 9 cm. Which of the options below can be the length of the third side?

Option 1: 17 cm

Option 2: 23 cm

Option 3: 24 cm

Option 4: 5 cm