A ladder is 74 feet tall. Its base must be at least 24 feet from the wall. If each story is 10 feet, what is the highest story it can reach?

Question

This is an algebra problem (inequalities) I am stuck on (my mom can only solve it using pythagorean theoreom, and my brother using trigonometry,neither of which I know):

Answer 1

Hi Tracy!

 

This question requires  a bit of logic. It took me some time to figure it out. Lol. Anyways here it goes.

 

Each story is 10 feet so this means the ladder would reach the 7th story when its height gets 70 feet. To get to the 8th story it should be 6 feet longer than its height which is 74 feet. So in other words it is 8th story = 80 feet ladder. 

 

So the highest this ladder could reach is the 7th story or the 7th floor of the building.

 

Now you can check it using Pythagorean theorem:

 

72² = 24² -x²

 

5476 - 576 = x²

 

√4900 = √x²

 

70 = x

 

70 feet height of the building represents 7th story.

 

 

I hope this helps!

 

Regards, 

 

Fatima K.