Stuck on another math problem

[SkyHog]

Ok - I am drawing a blank, possibly because it is 5:07am and I am extremely tired, or because I am just an idiot with this stuff, but I can't quite figure this one out.

3. The Foot of an extension ladder is 9 feet from a wall. The height that the ladder reaches on the wall and the length of the ladder are consecutive integers. How long is the ladder? Be sure to show your work. Remember that no work means no credit.

I figure it starts with a^2 + b^2 = c^2 , or in the context of this problem, a^2 + b^2 = (b^2 + 1)^2.

I then figure that I can add in the nine and get:

9^2 + b^2 = (b^2 + 1)^2 or
81 + b^2 = (b^2 + 1)(b^2 + 1) or
81 + b^2 = b^4 + 2b^2 + 1 or
b^4 + b^2 -80 = 0

I am now lost. I can factor out a b^2 from the first part and get
b^2(b^2 + 1) - 80 = 0

But I don't even see where I can go from there. I can tell its going to have 2 solutions because its been set to equal 0, but I am lost.

Any help?

 

[EdFred]

Pyth Theorem:
a^2 + b^2 = c^2
Known:
c = b + 1

Substitute:

a^2 + b^2 = (b+1)^2

Expand

a^2 + b^2 = b^2+2b+1

b^2 cancel out

a^2 = 2b+1
81=2b+1
80=2b
b=40
c=41


I'll blame the 5:00 am for you squaring the b twice on the right side.

 

[SkyHog]

Pyth Theorem:
a^2 + b^2 = c^2
Known:
c = b + 1

Substitute:

a^2 + b^2 = (b+1)^2

Expand

a^2 + b^2 = b^2+2b+1

b^2 cancel out

a^2 = 2b+1
81=2b+1
80=2b
b=40
c=41


I'll blame the 5:00 am for you squaring the b twice on the right side.

Oh....duh! Thanks man. I dunno why I thought c would be b^2+1, expecially considering in my let statement, I let c=b+1

De de de!

 

[Carol]

a² + b² = c²

a² = 9
c² = (b + 1)²

9 + b² = (b + 1)²
9 + b² = b² + 2b + 1
9 = 2b + 1
8 = 2b
4 = b

a = 3
b = 4
c = 5

a² = 9
b² = 16
c² = 25

 

[EdFred]

a² + b² = c²

a² = 9
c² = (b + 1)²

9 + b² = (b + 1)²
9 + b² = b² + 2b + 1
9 = 2b + 1
8 = 2b
4 = b

a = 3
b = 4
c = 5

a² = 9
b² = 16
c² = 25

Carol -

You might want to read the question again

 

[Carol]

Carol -

You might want to read the question again

ah, yes

My answer reflects a question stating:

"...the square root of one unknown length is one integer greater than the square root of the other unknown length..."

Is it safe to put the base of a forty-foot ladder only nine feet away from a wall?

 

[Michael]

so what your saying then is...algebra is only good if you need to know how far off the ladder your going to fall.

 

[Carol]

Re: ladder safety thread hijack

TMI ...

Proper climbing angle for a ground ladder is approximately 75°. Place the base of the ladder a distance of ¼ the length extended. Less than this angle lowers the capacity of the ladder, and a closer position increases your chances of falling off as the angle is too steep.

from http://www.wfrfire.com/website/articles/ladsafe.htm

Those mathbook writers probably run with scissors too.