Help with DAT question of the day Math Q!!

[Lisa Lai]

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Hey there guys,

I signed up for the DAT Question of the day a while back and have been receiving them every since. They're a really good way to refresh the studying.

I ran into trouble with one of the math questions. Here it is:

If the area and perimeter of a right triangle are 30 cm squared and 30 cm respectively, what is the length of the hypotenuse?
A) 9; B) 11; C) 12; D) 13; E) 15

I am not quite sure how they got to the answer....they say that you have to use the equations 1/2ab = 30 cm squared, a+b+c = 30, and a squared + b squared = c squared. How would I go about solving it?

Thanks in advance!!!! 🙂

 

[andrewhntran]

Never mind, i know where I went wrong lol, I was thinking its 30 squared

 

[JtotheEdoubleF]

Ok read what I have to say carefully... it might help to write it down. The answer has to be greater than 14, leaving choice e. A x B is equal to half of 30 right. This means a x b is 15. Knowing that a plus b plus c equals 30, we can logically figure this out. Lets pick two numbers close to each other for a and b. Lets estimate and pick 4 and 4. A x B would then give us 16, which is just shot off of 15. Now, this would mean that c would be 22 since a and b add to 8 and to get to 30 we need to add 22 (a plus b equals c). That is wayyyy too high. NOW, the only way to reduce the possible value of C is to pick two numbers for A and B far from each other. The farthest they can be is 15 and 1 (by respecting that A x B is 15). SO NOW what does this all mean? If A is 1 and b is 15 and A plus B plus C equals 30, C would have to be 14, and that is the smallest possible number C can be. Leaving choice E as your answer. P.S. I can be COMPLETELY wrong about this. Logic doesn't always work in math... especially in combinations and permutations

 

[Ari Rezaei]

You know, I was telling someone else the easiest way to solve this would be plug and chug. Solving this algebraically would be a nightmare on the DAT. If you ever see a triangle question on the DAT, it tends to be a pythagorean triple:
3,4,5
5,12,13
7,24,25, etc.

It happens that this follows that rule, and by guessing pythagorean triples you find out the answer is 13 and works perfect in all 3 equations.

 

[andrewhntran]

Ok, so I'm pretty sure this is the solution after fixing the stupid mistake that I made.
I know we shouldn't do this on the DAT, but just in case you are curious how to get the answer mathematically

 

[JtotheEdoubleF]

But 5 times 12 does not equal 15

 

[JtotheEdoubleF]

Unless I misunderstood that 1/2ab = 30 squared actually means 30 squared and not 30 square cm

 

[andrewhntran]

that's what I misunderstood the first time I solved it, It should actually be 30 (square cm)

 

[JtotheEdoubleF]

Forget everything I said. Since 1/2 A x B is 30.... A x B would be 60!!! Not 15... lol. Its late. Been studying bio destroyer all day... lol

 

[JtotheEdoubleF]

Good job Andrew, lol I didn't see the update

 

[Lisa Lai]

Thank you all for your help! Much appreciated 🙂

 

[Lisa Lai]

I had meant 30 cm squared but had written in 30 squared. I should have clarified it. Sorry for the misunderstanding!