+0  
 
0
42
1
avatar

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
 #1
avatar+850 
+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 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.   

.

 Jul 2, 2023

5 Online Users

avatar
avatar