SOLUTION: A ladder is leaning against a house and the base of the ladder is 15 feet from the house. When the bottom of the ladder is pulled 9 feet farther away from the house, the upper end
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Question 337650: A ladder is leaning against a house and the base of the ladder is 15 feet from the house. When the bottom of the ladder is pulled 9 feet farther away from the house, the upper end of the ladder slides 13 feet down. How long (in feet) is the ladder?
DRAW YOU LADDER AND LABLES TO YOUR PYTHAGOREAN THEOREM:
A^2+B^2=C^2
FIRST LADDER: C^2=24^2+A^2
SECOND LADDER: C^2=15^2+(A+13)^2
PLUG IN: 24^2+A^2 = 15^2+(A+13)^2
24^2+A^2 = 15^2+(A+13)(A+13)
24^2+A^2 = 15^2+A^2+26A+13^2
24^2+A^2-A^2 =15^2+A^2+26A+13^2-A^2
24^2 = 15^2+26A+13^2
24^2-15^2-13^2= 26A
576-225-169 = 26A
182/26 = A
A = 7 FEET
GO BACK AND PLUG IN THE THEOREM FOR EACH LADDERS FOR VARIFICATION.
C^2=24^4 + A^2 C^2=576+7^2=49+576=625
C=SQRT625 = 25 SO THE LADDER IS 25 FEET ANSW.( DO FOR THE OTHER TOO SHOULD BE THE SAME... C^2=15^2+(A+13)^2) Found 2 solutions by nerdybill, chiexpert:Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! A ladder is leaning against a house and the base of the ladder is 15 feet from the house. When the bottom of the ladder is pulled 9 feet farther away from the house, the upper end of the ladder slides 13 feet down. How long (in feet) is the ladder?
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Draw a diagram of the problem. It'll help you see the solution.
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Apply Pythagorean theorem:
Let x = length of ladder
and
Let y = upper end of ladder when it is 15 ft from house
then we have two equations:
x^2 = 15^2 +y^2
x^2 = 24^2 + (y-13)^2
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Solve for y:
15^2 +y^2 = 24^2 + (y-13)^2
225 +y^2 = 576 + (y-13)(y-13)
225 +y^2 = 576 + y^2-26y+169
225 +y^2 = y^2-26y+745
225 = -26y+745
-520 = -26y
20 ft = y
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Plug the above into equation 1 and solve for x:
x^2 = 15^2 +y^2
x^2 = 15^2 +20^2
x^2 = 225 + 400
x^2 = 625
x = 25 feet (length of ladder)
You can put this solution on YOUR website! DRAW YOU LADDER AND LABLES TO YOUR PYTHAGOREAN THEOREM:
A^2+B^2=C^2
FIRST LADDER: C^2=24^2+A^2
SECOND LADDER: C^2=15^2+(A+13)^2
PLUG IN: 24^2+A^2 = 15^2+(A+13)^2
24^2+A^2 = 15^2+(A+13)(A+13)
24^2+A^2 = 15^2+A^2+26A+13^2
24^2+A^2-A^2 =15^2+A^2+26A+13^2-A^2
24^2 = 15^2+26A+13^2
24^2-15^2-13^2= 26A
576-225-169 = 26A
182/26 = A
A = 7 FEET
GO BACK AND PLUG IN THE THEOREM FOR EACH LADDERS FOR VARIFICATION.
C^2=24^4 + A^2 C^2=576+7^2=49+576=625
C=SQRT625 = 25 SO THE LADDER IS 25 FEET ANSW.( DO FOR THE OTHER TOO SHOULD BE THE SAME... C^2=15^2+(A+13)^2)
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