SOLUTION: The base of a triangle is 8cm greater than the height. The area is 42cm^2. Find the height and length of the base. How do I set up this problem to get the answer?

Question 176017: The base of a triangle is 8cm greater than the height. The area is 42cm^2. Find the height and length of the base. How do I set up this problem to get the answer?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let b=base and h=height

"The base of a triangle is 8cm greater than the height" means that

Start with the area of a triangle formula

Plug in (the given area) and

Multiply both sides by 2.

Multiply

Rearrange the terms.

Distribute

Subtract 84 from both sides.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for h

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible answers are or

However, since a negative height is not possible, this means that is NOT a solution

So the only answer for the height is which means that the height is 6 cm.

Go back to the first equation

Plug in

Add. So the base is 14 cm.

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Answer:

So the base is 14 cm and the height is 6 cm
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