The length of XY is approximately 12.5 centimeters when the hypotenuse XZ is 13 cm and the base ZY is 4 cm.
To determine the length of XY using the Pythagorean theorem, we employ the formula:
XY = sqrt((XZ)^2 - (ZY)^2)
Given that the hypotenuse XZ is 13 cm and the base ZY is 4 cm, we substitute these values into the formula:
XY = sqrt(13^2 - 4^2)
XY = sqrt(169 - 16)
XY = sqrt(153)
Calculating the square root of 153, we get:
XY is approximately 12.5 cm (1 decimal place).