The top of a ladder leans against a house at a height of 12 feet. The length of the ladder is 8 feet more than the distance from the house to the base of the ladder. Find the length of the ladder?

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The top of a ladder leans against a house at a height of 12 feet. The length of the ladder is 8 feet more than the distance from the house to the base of the ladder. Find the length of the ladder?

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Answer 1 · 2016-03-19T00:56:30

$13 f t$ $13ft$

Explanation:

magoosh

The ladder leans against a house at a height $A C = 12 f t$ $AC=12 ft$
Suppose distance from the house to the base of ladder $C B = x f t$ $CB=xft$
Given is that length of ladder $A B = C B + 8 = (x + 8) f t$ $AB=CB+8=(x+8) ft$
From Pythagorean theorem we know that
$A B^{2} = A C^{2} + C B^{2}$ $AB^2=AC^2+CB^2$ , inserting various values
${(x + 8)}^{2} = 12^{2} + x^{2}$ $(x+8)^2=12^2+x^2$
or $cancel(x^2)+16x+64=144+cancel(x^2)$
or $16x=144-64$
or $16x=80/16=5$
Therefore length of ladder $=5+8=13ft$

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Alternatively, one can assume length of ladder $AB=xft$
This sets the distance from the house to the base of ladder $CB=(x-8)ft$
Then proceed with setting up of equation under Pythagorean theorem and solve for $x$

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The top of a ladder leans against a house at a height of 12 feet. The length of the ladder is 8 feet more than the distance from the house to the base of the ladder. Find the length of the ladder?

1 Answer

Explanation:

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