Hi Bruce,

This is an application of Pythagoras' Theorem which states

For any right triangle the square on the hypotenuse is the sum of the squares on the other two sides.

The hypotenuse is the side opposite the right angle and the statement means

For any right triangle the area of the square on the hypotenuse is the sum of the areas of the squares on the other two sides.

Hence in the diagram below the area of the red square is the sum of the areas of the green squares.

Algebraically if the lengths of the sides of the triangle are a, b and c where c is the length of the hypotenuse then

c² = a² + b²

In the situation you describe a = 34 and b = 31 so

c² = 34² + 31² = 1156 + 961 = 2117

and hence

c = sqrt(2117) = 46.01 to two decimal places.

Penny

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