Question

The length of segment XY is 9 cm. Which statements regarding triangle XYZ are correct? Check all that apply.

Answer 1

Answer-

• YZ = 9 cm
• $XZ=9\sqrt2$
• XZ is the longest segment in triangle XYZ.

Solution-

Triangle XYZ is a right angle triangle with ∠Y=90°

Triangle XYZ is also an isosceles triangle, as

∠X =45°= ∠Z

Therefore, triangle XYZ is a right angle isosceles triangle.

So,

XY = YZ = 9 cm

Applying Pythagoras theorem,

$\Rightarrow XZ^2=XY^2+YZ^2\\\\\Rightarrow XZ^2=9^2+9^2\\\\\Rightarrow XZ^2=2\times 9^2\\\\\Rightarrow XZ=\sqrt{2\times 9^2}=9\sqrt2$

In a right angle triangle, always the hypotenuse is the largest. So XZ is the longest segment in triangle XYZ.

Answer 2

The length of segment XY is 9 cm. Which statements regarding triangle XYZ are correct? Check all that apply.

YZ = 9 cm 

XZ = 9√2cm