The two shortest sides of a window shaped like a right triangle measure 24 centimeters and 32 centimeters. Bonnie wants to put a wooden frame around its edges. How many centimeters of wood are needed for the fame?

We need the 3 sides length of the triangle, we have 2 of them, the cathetuses they are because it is stated they are the shortest sides of a right triangle, the biggest side is the hypothenuse. We know from Pythagoras theorem that the sum of the square of the cathetuses of a right triangle are equal to the hypothenuse squared, if we call a, b to the cathetuses, that is:

hyp^2 = a^2 + b^2

and if we substitute the data we have:

hyp^2 = (24) ^2 + (32) ^2

hyp^2 = 1600

hyp = √1600

hyp = 40

So the lengths of the triangle sides are 24, 32 and 40 cm

Therefore the frame needs:

24 + 32 + 40 = 96

96 cm of wood for the frame are needed