SOLUTION: The product of two consecutive positive odd integers is one less than three times their sum. Find the integers. A ladder is resting against a wall. The top of the ladder touch

Question 235999: The product of two consecutive positive odd integers is one less than three times their sum. Find the integers.

A ladder is resting against a wall. The top of the ladder touches the wall at a height of 12 feet. Find the length of the ladder if the length is 8 feet more than its distance from the wall.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let

represent a positive odd integer. Then the next consecutive positive odd integer must be

.

The product:

The sum:

One less than that:

Which is to say:

Solve the quadratic (it factors). Exclude the negative root because the problem asked for positive odd integers. The positive root is one of the integers. Add 2 to get the other one.
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The ladder, the ground, and the wall, presuming that the wall and the ground form a right angle, form a right triangle with sides 12, and

, and hypotenuse

Mr. Pythagoras says:

Solve for

John

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