Math problem any help?

Question

A ladder is leaning against a building. The distance from the bottom of the ladder to the building is 8 ft less than the length of the ladder. How high up the side of the building is the top of the ladder if that distance is 4 ft less than the length of the ladder?

Answer 1

Let X be the length of the ladder.

Using the Pythagoras theorem,we get(from the information given in the problem),

(X-8)^2 + (X-4)^2 = X^2

or,X^2 + 64 - 16X + X^2 + 16 - 8X = X^2

or, X^2 - 24X + 80 = 0

This is a quadratic equation.Solve it to get X.The required answer is (X-4)

Answer 2

I don't know what kinda math class your in, but here goes

we will use "L" as the unknown length of the ladder

[(L-8ft)x(L-8ft)] + [(L-4ft)x(L-4ft)]= LxL  

so your answer is the square root of [(L-4ft)x(L-4ft)]  

or just (L-4ft)

If you are required to have a definate value....I will have to brush up on my own math skills.

16ft is the answer

Answer 3

(x-8)^2 + (x-4)^2 =x^2

find x

Answer 4

Let length of ladder be x ft.

dist. from the bottom to the building = (x – 8)

dist. from bottom to top = (x – 4)

It forms a right angle triangle

x² = (x– 8)² + (x – 4)²

x² = x² – 16x + 64 + x² – 8x + 16

x² – 24x + 80 = 0

(x – 20)(x – 4) = 0

x = 20 or x = 4 ------- not possible

x = 20 ft. length of ladder.

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