# Pythagorean Theorem

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A ladder resting against the side of a building reaches 32 ft up the building. If the ladder is 40 ft long, how far from the building is the base of the ladder?

• Pythagorean Theorem -

Draw the problem out, with a ladder leaning against the wall, and label the respective lengths. You will notice it forms a right-angle triangle, with the ladder as the hypotenuse.

So the theorem is
a^2+b^2 =c^2

where c represents the ladder length (the hypotenuse), and so a can represent the distance of the ladder from the base of the building (the answer), and b is where the ladder reaches on the building.

Therefore,
a^2+32^2=40^2

Since a is what we need, rearrange the above formula to solve for a and you will get your answer. (Remember the units ft)

• Pythagorean Theorem -

24 ft

• Pythagorean Theorem -

The doorway of the family room measures 6 1/2 feet by 3 feet. What is the length of the diagonal of the doorway?

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