What is the exact length of the diagonal of a 10 cm by 15 cm rectangle?

To solve this, use pythagorean theroem:

a^2 + b^2 = c^2

Since the diagonal is across from the right angle, it is represented as c.

10^2 + 15^2 = c^2
100 + 225 = c^2
325 = c^2
sqrt 325 = c

Converting to simplest radical form:
5 * sqrt 13 = c

Hope this helps!

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