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# Pythagorean Theorem

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A 25 foot ladder leans against a vertical wall. The foot of the ladder is 7 feet from the base of the wall. If the top of the ladder slips 4 feet down the wall, how far will the foot of the ladder slide?

Jul 2, 2023

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A 25 foot ladder leans against a vertical wall. The foot of the ladder is 7 feet from the base of the wall. If the top of the ladder slips 4 feet down the wall, how far will the foot of the ladder slide?

One way to do this is to use Pythagoras' Theorem twice.  Sort of a before and after.

This would be much better if I could just draw the pictures.  But I can't, so here goes...

Visualize the ladder as the hypotenuse of a right triangle.

Then the hypotenuse is 25 and the ground side is 7.

By the theorem a2 + b2 = c2, then    a2 (the wall)  =  c2 (the ladder) – b2 (the ground)

a2  =  252 – 72

a2  =  625 – 49  =  576

a  =  sqrt(576)  =  24 (the height of the wall side)

When the ladder slips 4 feet down the wall, the new "a" becomes 20

The hypotenuse stays the same 25 because it's a ladder

So now we can say                         b2 (the ground)  =  252 (the ladder) – 202 (the wall)

b2  =  625 – 400  =  225

b  =  sqrt(225)  =  15 (the length of the ground side)

When the top of the ladder slid down the side of the wall 4 feet,

the bottom of the ladder slid out until it was 15 feet from the wall.

The ladder was already 7 feet from the wall, so the bottom of the ladder slid 8 feet.

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Jul 2, 2023