Question

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.)

Answer 1

And please can you show me all your work.

Answer 2

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!