SOLUTION: Help! My final is on Monday and I can't figure out this word problem. Please write it out step by step so I will be able to do it on the final. Thank you. The height of a triangle

Question 173140: Help! My final is on Monday and I can't figure out this word problem. Please write it out step by step so I will be able to do it on the final. Thank you.
The height of a triangle is 8 centimeters greter than the base. The area of the triangle is 90 square centimeters. Find the length of the base and height of the triangle. Define a variable. Set up a quadratic equation. Solve. Show all work.
I'm really stuck, I thought I knew it but I've been at it most of the day.
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let b=base and h=height

Since "The height of a triangle is 8 centimeters greter than the base", this means that

Also, remember that the formula for the area of a triangle is

Since the "area of the triangle is 90 square centimeters", this tells us that

Plug in (the given area) and

Multiply both sides by 2

Multiply

Distribute

Subtract 180 from both sides.

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

Let's use the quadratic formula to solve for b

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 lengths of the base are or

However, a negative base does NOT make sense. So this means that the only possible length for the base is

So the base is 10 centimeters.

Go back to the height equation (remember the height is 8 cm longer than the base)

Plug in

Add

So the height is 18 cm

===============================================================

Answer:

So the base is 10 cm and the height is 18 cm.

Check:

Area:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let base =
height =

multiply both sides buy

Complete the square

take square root of both sides

The base is 10 cm and the height is 18 cm
check:

OK
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