Question : In $\triangle X Y Z, \angle YXZ=90°$, P is a point on side YZ such that XP is perpendicular to YZ. If XP = YP = 10 cm then what will be the value of PZ?

Option 1: 8 cm

Option 2: 9 cm

Option 3: 12 cm

Option 4: 10 cm

Question : X, Y, and Z are three equilateral triangles. The sum of the areas of X and Y is equal to the area of Z. If the side lengths of X and Y are 6 cm and 8 cm respectively, then what is the side length of Z?

Option 1: 10 cm

Option 2: 10.5 cm

Option 3: 9.5 cm

Option 4: 9 cm

Question : In $\triangle$ABC, Z is a point on side BC, and AB = AC. If $\angle$AZB = 90° and BC = 42 cm, then what will be the length of BZ?

Option 1: 21 cm

Option 2: 32 cm

Option 3: 28 cm

Option 4: 35 cm

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 : If $x : y$ is the ratio of two whole numbers and $z$ is their HCF, then the LCM of those two numbers is:

Option 1: $yz$

Option 2: $\frac{xz}{y}$

Option 3: $\frac{xy}{z}$

Option 4: $xyz$