SOLUTION: A 14 foot ladder leans against the side of a house. How high does the ladder reach if the distance between the bottom of the ladder and the house is 11 feet less then the distance

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 Question 118843: A 14 foot ladder leans against the side of a house. How high does the ladder reach if the distance between the bottom of the ladder and the house is 11 feet less then the distance between the top of the ladder and the ground.Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!X^2+(X-11)^2=14^2 X^2+X^2-22X+121=196 2X^2-22X+121-196=0 2X^2-22X-75=0 USING THE QUADRATIC EQUATION: WE GET: X=(22+-SQRT[22^2-4*2*-75])/2*2 X=(22+-SQRT484+600])/4 X=(22+-SQRT1084)/4 X=(22+-32.924)/4 X=(22+32.924)/4 X=54.924/4 X=13.73 IS THE DISTANCE FRON THE GROUND TO THE TOP OF THE LADDER. PROOF 13.73^2+(13.73-11)^2=196 188.5+7.5=196 196=196