Right Triangle Question

spadda

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May 24, 2011
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Hey guys,
i've been stumped on another questions

"A right triangle has a base that is 2 more than twice the height. Find the Length of the base of the triangle if the area is 30 square units."

i understand that for a right triangle
Area = 1/2 Length x Width

30 Units = 1/2 (2... im stumped at this part making the equation... any help?

thanks :D
 
spadda said:
Hey guys,
i've been stumped on another questions

"A right triangle has a base that is 2 more than twice the height. Find the Length of the base of the triangle if the area is 30 square units."

i understand that for a right triangle
Area = 1/2 Length x Width

30 Units = 1/2 (2... im stumped at this part making the equation... any help?

thanks :D
tkhunny would tell (and it is excellent advice) first NAME each unknown, which means assign a unique letter to each unknown in your problem. Whenever you seem to be stuck in a word problem, that is always the first thing to do. So, what are your unknowns and how do you want to name them?
 
the unknown would be the base ... x
1/2 * (2 + 2x ) * x = 30
= 1 + x = 30
x = 29... wrong??
 
spadda said:
the unknown would be the base ... x
1/2 * (2 + 2x ) * x = 30
= 1 + x = 30
x = 29... wrong??
First, it is an excellent habit to learn to check your own work.
Is it true that (1/2) * 29 * (58 + 2) = 30 * 29 = 30?

No. So you made a mistake somewhere.

Technically you did make a mistake when you named the base x and then implicitly named height as (2 + 2x) because that is not what the problem says, but it turns out the mistake is harmless. Let's fix it just to be careful for the future.

Name all the unknowns and variables.
Let x = the height.
So the base = b = (2 + 2x).
Let the area = A = 30.

Now we use the formula for area just as you did and get 30 = A = (1/2) * b * x = (1/2) * (2 + 2x) * x, which is identical to your equation.

So the problem must be in how you solved the equation. Please give it another try.
 
x = 1/2 ( 2 + 2x) x
x = 1/2 * (2x + 2x^2)
x= x + x^2
... im stuck at this, i seem to be doing something really really wrong?
 
spadda said:
x = 1/2 ( 2 + 2x) x
x = 1/2 * (2x + 2x^2)
x= x + x^2
... im stuck at this, i seem to be doing something really really wrong?
WHOA

Area = A = (1/2) * b * x.
b = (2 + 2x).
A = ???????

This is why it is IMPORTANT to WRITE down what EACH variable and unknown is.
x = (1/2) * (2 + 2x) * x means that the height = A. That is NOT the problem statement.
You will have no problem with math if you take it step by step.
Step 1. Write down what symbols represent EACH of your unknowns and variables. (Experience will help you determine how to choose the best symbols; for example, I would have chosen h = height, b = base, then b = (2 + 2h) is obvious. But choosing x is not WRONG, just not convenient.)
Step 2. Write down what the GIVEN relationships are among those unknowns and variables, using the symbols that you select and math notation.
Step 3. Then manipulate the symbols to find the unknowns. Step 3 is entirely mechanical once you know the proper techniques.
That is how to solve EVERY word problem in the UNIVERSE.

So, you need to solve A = 30 = (1/2) * (2 + 2x) * x = ????

You CAN do this. Just need to stay calm and focused. No big deal. Talk to you tomorrow.
 
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