SOLUTION: A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the dista

Algebra.Com
Question 165009: A ladder is leaning against a wall. The distance from the bottom of the ladder to the wall is 3 feet less than the length of the ladder. Find the length of the ladder, if the distance of its top to the ground is 4 feet less than the length of the ladder.

Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
Draw a picture of the problem -- label everything you know -- this helps!
.
Let x = length of the ladder
x-3 = distance from the bottom of the ladder to the wall
x-4 = distance of its top to the ground
.
Since the wall the the ground forms a right angle, this is a "right triangle". We can apply Pythagorean theorem:
(x-3)^2 + (x-4)^2 = x^2
x^2-6x+9 + x^2-8x+16 = x^2
2x^2-14x+25 = x^2
x^2-14x+25 = 0
Since we can't factor, we must resort to the quadratic formula. Doing so, will result in:
x = {11.90, 2.10}
.
We can toss out the 2.10 answer leaving us with:
11.90 feet (length of the ladder)
.
Details of quadratic:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=96 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 11.8989794855664, 2.10102051443364. Here's your graph:
RELATED QUESTIONS

A ladder is leaning against a wall. The distance from the bottom of the ladder to the... (answered by ankor@dixie-net.com)
A ladder is leaning against a wall. The distance from the bottom of the ladder to the... (answered by nerdybill)
a ladder is leaning against a building.the distance from the bottom of the ladder to the... (answered by mananth)
A ladder is leaning against a wall. The distance from the bottom of the ladder to the... (answered by vleith)
A ladder is resting against a wall. The top of teh ladder touches the wall at a height of (answered by Earlsdon)
A 13 ft ladder is leaning against a wall . The distance from the top of the ladder to the (answered by algebrahouse.com,MathTherapy)
Ok, I'm not good at word problems and I need a little help if possible. A ladder is... (answered by checkley75)
7. A 20-feet ladder is leaning against a wall where the top of the ladder is 18 feet from (answered by josgarithmetic)
A ladder is resting against a wall. The top of the ladder touches the wall at a height of (answered by MathLover1)