Posted by **Jack ** on Thursday, February 28, 2013 at 7:11pm.

A ladder is resting against a wall. The top of the ladder touches the wall at a height of 15 feet and the length of the ladder is one foot more than twice the distance from the wall. Find the distance from the wall to the bottom of the ladder. (Hint: Use the Pythagorean Theorem.)

- Algebra 1 -
**Jack **, Thursday, February 28, 2013 at 7:12pm
And please can you show me all your work.

- Algebra 1 -
**Reiny**, Thursday, February 28, 2013 at 9:52pm
make a sketch.

let the distance of the foot from the wall be x ft

label the base x

the length of the ladder (the hypotenuse) is

one foot more than twice the distance from the wall

---- 2x + 1

mark the hypotenuse 2x + 1

and of course the height is 15

so in your right-angled triangle

15^2 + x^2= (2x+1)^2

225 + x^2 = 4x^2 + 4x + 1

0 = 3x^2 + 4x - 224

Using the quadratic formula:

x = (-4 ± √2704)/6

= (-4 ± 52)/6

= 8 or a negative, which we would reject

So the ladder is 8 ft from the wall

check:

height = 15

base = 8

ladder = 17

is 15^2 + 8^2 = 17^2 ?? , YES!

## Answer this Question

## Related Questions

- algebra - A ladder is resting against a wall. The top of the ladder touches the ...
- math- solving quadratic equations by factoring - a ladder is resting against a ...
- algebra 2 - a ladder is resting against a wall. the top of the ladder touches ...
- math - A ladder is resting against a wall. The top of the ladder touches the ...
- maths - A ladder lies against a wall.the top of the ladder reaches 8feet above ...
- MAth - A 13 foot ladder is resting against the wall. The bottom is initially 10 ...
- math - A ladder is resting against a wall. the foot of the ladder is 8 feet from...
- math - a ladder rests against the top of a wall. The head of a person 3.5 feet ...
- Calculus - related rates: a ladder, 12 feet long, is leaning against a wall. if ...
- math - A ladder leans against a brick wall, The top of the ladder touches the ...

More Related Questions