Answer
XY = 30 cm
Step-by-step explanation
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this question,
a = XY = ?
b = YZ = 72 cm
hyp = XZ = 78 cm
a² + b² = (hyp)²
XY² + 72² = 78²
XY² + 5184 = 6084
XY² = 6084 - 5184
XY² = 900
We then take the square root of both sides
√(XY²) = √900
XY = 30 cm
Hope this Helps!!!