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?

Guest Jul 2, 2023

#1**+1 **

*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 a^{2} + b^{2} = c^{2}, then **a ^{2}** (the wall)

a^{2} = 25^{2} – 7^{2}

a^{2} = 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 **b ^{2}** (the ground)

b^{2} = 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**.

_{.}

Bosco Jul 2, 2023