Question

Tom is building a barn 30 feet wide and 40 feet long. He has his footer laid out. How long is thediagonal of the footer if the building is square?

Answer 1

We can draw the barn and its footer, seen from the top, as:

If the footer is square, is has the same side length for all four sides.

The footer is placed across the width of the barn, so its side length is 30 feet.

The diagonal H can be calculated with the Pythagorean theorem as:

`\begin{gathered} H^2=30^2+30^2 \\ H^2=2\cdot30^2 \\ H=\sqrt[]{2\cdot30^2} \\ H=30\sqrt[]{2} \\ H\approx30\cdot1.414 \\ H\approx42.426 \end{gathered}`

Answer: the diagonal is 42.426 feet long.