At the base of the straight prism lies a square. the diagonal of the prism is 17 cm and the height is 15 cm.

At the base of the straight prism lies a square. the diagonal of the prism is 17 cm and the height is 15 cm. Find the length of the diagonal of the side face of the prism.

In a right-angled triangle AA1C, according to the Pythagorean theorem, we determine the length of the leg AC.
AC ^ 2 = A1C ^ 2 – AA1 ^ 2 = 17 ^ 2 – 15 ^ 2 = 289 – 225 = 64.
AC = 8 cm.
AC is the diagonal of the ABCD square, AC = AD * √2.
AD = AC / √2 = 8 / √2 = 4 * √2 cm.
From the right-angled triangle AA1D, by the Pythagorean theorem, we define the hypotenuse DA1.
DA1 ^ 2 = AD ^ 2 + AA1 ^ 2 = (4 * √2) ^ 2 + 15 ^ 2 = 32 + 225 = 257.
DA1 = √257 cm.
Answer: The diagonal of the side face of the prism is √257 cm.