Roger wants to build a bookend by combining three pieces of wood into the shape of a right triangle. the shortest piece of wood is to be 3 inches long. the next shortest piece of wood is to be x inches long. write an expression in terms of x that models the length, in inches, of the longest piece of wood.

We are given that the shortest side is 3 inches long and that the next shortest piece is x inches long. We want to get a formula to calculate the length of the longest side.

We are also given that the triangle would be a right-angled triangle. This means that the longest side would be the hypotenuse.

The formula used to get the side of the hypotenuse was discovered by Pythagoras and it is as follows:
(hypotenuse)^2 = (side1)^2 + (side2)^2
hypotenuse = sqrt [(side1)^2 + (side2)^2]

Applying this to the givens, the length of the longest side would be:
length of longest side = sqrt [(3)^2 + (x)^2]
length of longest side = sqrt [9 + x^2] inches