SOLUTION: Please help me solve this problem. The problem is that there are two ladder leaned up against a wall. One is 20m and the other is 15m. They both reach the same height up the wall.

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Question 135888: Please help me solve this problem. The problem is that there are two ladder leaned up against a wall. One is 20m and the other is 15m. They both reach the same height up the wall. The bottom of the 20m ladder is 7m farther from the building than the 15m ladder.
Answer by checkley77(12844) (Show Source):
You can put this solution on YOUR website!
X^2+Y^2=20^2 OR X^2=20^2-Y^2 (X) BEING THE HEIGHT UP THE WALL & (Y) BEING THE DISTANCE OF THE BOTTOM OF THE LADDER FROM THE BUILDING.
X^2+(Y-7)^2=15^2 OR X^2=15^2-(Y-7)^2
SETTING THE X^2 EQUATIONS EQUAL AND SOLVE FOR Y:
20^2-Y^2=15^2-(Y-7)^2
400-Y^2=225-Y^2+14Y-49
400=225+14Y+49
14Y=400-225+49
14Y=224
Y=224/14
Y=16 FEET IS THE DISTANCE FROM THE WALL TO THE BOTTOM OF THE 20 FOOT LADDER.
X^2+16^2=20^2
X^2+256=400
X^2=400-256
X^2=144
X=SQRT144
X=12 FEET IS THE DISTANCE UP THE WALL.
PROOF
(16-7)^2+12^2=225
9^2+144=225
81+144=225
225=225