Question 26524: A woman wants to put a ladder against the wall of her house and climb up to fix the gutter. The gutter is 14 feet above the ground. Unfortunately, there is an 8 feet high retaining wall standing 3 feet away from her house. The ladder can’t be placed between the retaining wall and the house, so it must be placed on the outside of the retaining wall. The ladder will go over the retaining wall (it can touch it) and then up to the roof. How long a ladder does she need?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Draw the picture.
You have similar triangles.
Larger triangle: height = 14; base = x+3
Smaller triangle: height = 8; base = x
Set up a proportion to find "x", as follows:
4/(x+3)= 8/x
Solve for x to get x=4 ft.
Now the larger base is 3+4=7' and height is 14'
Use Pytagoras to get hyp.^2=7^2+14^2
hyp^2=49+2401
hyp^2=2450
hyp=49.97 ft.
She need a ladder that is at least 49.97 ft, long.
Cheers,
Stan H.
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