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# The top of a ladder touches the wall at a height of 6 feet. Find the length of the ladder if the length is two feet more than its distance from the wall.

### 2 Answers by Expert Tutors

Anneliese A. | Proof-reading and writing improvement - fast, thorough, and reliableProof-reading and writing improvement - ...
5.0 5.0 (39 lesson ratings) (39)
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Picture this as a right triangle. The "distance from the wall" (i.e. the ground) is the bottom of the triangle, and the ladder is the hypotenuse. You are given the height as 6 ft, so this is the third side of the triangle.

Let x equal the ground / base of the triangle.

Because this is a right triangle, we can use the Pythagorean theorem (a2 + b2 = c2), where a and b are the two sides making the right angle, and c is the hypotenuse.

We are given in the problem that x is two feet more than the ladder / hypotenuse. So c = x+2. One side of triangle can be a, and the other b. Let's say that a is the height, which is given as 6, and b is the ground, which we are calling x:

a=6                       b=x                c=x+2

Plug this into the Pythagorean theorem:    62 + x2 = (x+2)2

First, simplify the right side by expanding it:
(x+2)2 = (x+2)(x+2) = x2 + 4x + 4
62 + x2 = 36 + x2 = x2 + 4x + 4

Subtract 4 from both sides: 32 + x2 = x2 + 4x

Subtract x2 from both sides: 32 = 4x

Divide both sides by 4: 8 = x

Remember that x was equal to the distance from the wall, and the length of the ladder is two feet more than x.

Therefore, the length of the ladder = x+2 = 8+2 = 10 feet.

Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
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One leg is 6 ft, the other leg is 8 ft. By Pythagorean triple {6, 8, 10}, the hypotunese must be 10 ft, which is the length of the ladder.