The foot of an extension ladder is 9 ft from a wall....

[silverdragon316]

Ladder location. The foot of an extension ladder is 9ft 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?

 

[jwpaine]

Well... Consecutive integers, would be like 15,16 or 20,21

So knowing the Pythagorean theorem, a^2+b^2 = c^2 I would say, for your problem, keeping consecutive integers in mind, that:

sqroot(9^2 + b^2) = c +/- b

This is my stab.. someone quote me if I'm wrong.

 

[axrw]

Picture the ladder leaned up against the wall. Notice that it looks like a right triangle? Remember the pythagorean theorem?

a^2 + b^2 = c^2

The legs of the triangle are 9ft out from the wall and the distance up the wall the ladder reaches, and the hypotenuse is the length of the ladder.

Now, the consecutive integer part makes it seem more complicated, but all it means is that one comes right after the other. So you can represent the smallest integer with x and the other with x + 1

I hope that helps enough to get you there.

Edit:jwpaine beat me to it.

 

[Denis]

Picture the ladder leaned up against the wall. Notice that it looks like a right triangle? Remember the pythagorean theorem?
a^2 + b^2 = c^2
The legs of the triangle are 9ft out from the wall and the distance up the wall the ladder reaches, and the hypotenuse is the length of the ladder.
Now, the consecutive integer part makes it seem more complicated, but all it means is that one comes right after the other. So you can represent the smallest integer with x and the other with x + 1

Yes; don't forget that the ladder = x+1, since hypotenuse is longest side;
so you have (x+1)^2 = x^2 + 9^2
x^2 + 2x + 1 = x^2 + 81
Can you finish it, hi yo silver ?