SOLUTION: The top of a 15ft ladder is 3ft farther up a wall than the foot of the ladder is from the bottom of the wall. How far is the foot of the ladder from the bottom of the wall?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The top of a 15ft ladder is 3ft farther up a wall than the foot of the ladder is from the bottom of the wall. How far is the foot of the ladder from the bottom of the wall?      Log On


   

Question 343301: The top of a 15ft ladder is 3ft farther up a wall than the foot of the ladder is from the bottom of the wall. How far is the foot of the ladder from the bottom of the wall?
Found 2 solutions by edjones, MathTherapy:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
The ladder is the hypotenuse of a right triangle with a base x and altitude x+3.
x^2+(x+3)^2=15^2
x^2+x^2+6x+9=225
2x^2+6x-116=0
x^2+3x-58=0
x=6.262...' see below
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Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-58+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A1%2A-58=241.

Discriminant d=241 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+241+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+241+%29%29%2F2%5C1+=+6.26208734813001
x%5B2%5D+=+%28-%283%29-sqrt%28+241+%29%29%2F2%5C1+=+-9.26208734813001

Quadratic expression 1x%5E2%2B3x%2B-58 can be factored:
1x%5E2%2B3x%2B-58+=+1%28x-6.26208734813001%29%2A%28x--9.26208734813001%29
Again, the answer is: 6.26208734813001, -9.26208734813001. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-58+%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
The top of a 15ft ladder is 3ft farther up a wall than the foot of the ladder is from the bottom of the wall. How far is the foot of the ladder from the bottom of the wall?

Let the distance from the bottom of the wall to the bottom of the ladder be B

Since the top of the ladder is 3ft farther up the wall than the foot of the ladder is from the base of the wall, then the ladder is (B + 3) ft up the wall

Using pythagorean, we get B%5E2+%2B+%28B+%2B+3%29%5E2+=+15%5E2
B%5E2+%2B+B%5E2+%2B+6B+%2B+9+=+225
2B%5E2+%2B+6B+-+216+=+0
2%28B%5E2+%2B+3B+-+108%29+=+2%280%29
B%5E2+%2B+3B+-+108+=+0
(B + 12)(B - 9) = 0_____Factoring equation
B + 12 = 0 OR B - 9 = 0

B = - 12 (ignore), or B = 9

Therefore, B, or the distance from the bottom of the ladder to the base of the wall is: highlight_green%288%29 feet.