QR question: Math Destroyer Test#9: #18

[HannibalLecter]

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The endpoints of the diagonal of a rectangle are located at (2,3) and (7,10). If the width of the rectangle is sqrt(10) what is the length?

I understand the answer how we can get the diagonal but I wanted to shave time and try a ratio solution but it doesn't work can anyone explain why:

Since its a diagonal we are talking about in this case of the rectangle. And, we are given the width. I just did a ratio of width to length (x) to the actual x and y values of the diagonal

(sqrt(10)/x)) = (5/7)
Get it?

But the answer is different but Im thinking the logic is right, why doesn't this work?

 

[AlbinoPolarBear]

The endpoints of the diagonal of a rectangle are located at (2,3) and (7,10). If the width of the rectangle is sqrt(10) what is the length?

I understand the answer how we can get the diagonal but I wanted to shave time and try a ratio solution but it doesn't work can anyone explain why:

Since its a diagonal we are talking about in this case of the rectangle. And, we are given the width. I just did a ratio of width to length (x) to the actual x and y values of the diagonal

(sqrt(10)/x)) = (5/7)
Get it?

But the answer is different but Im thinking the logic is right, why doesn't this work?

The diagonal and the 2 sides make up a right triangle.
Find the diagonal length, which is root74

d^2 = l^2 + w^2
74 = l^2 + 10
l = root64 = 8

For similar triangles, you can only compare 2 sides, not 3.

 

[AlbinoPolarBear]

Oh, Okay. I see what you're trying to do.

Nope, guess it doesn't work lol.

 

[HannibalLecter]

Hahaha I was just drawing a picture to show you but this is A VERY POORLY worded problem. Because the width of the rectangle can never be sqrt(10) if you actually look at a rectangle with a diagonal with those endpoints.

 

[AlbinoPolarBear]

Hahaha I was just drawing a picture to show you but this is A VERY POORLY worded problem. Because the width of the rectangle can never be sqrt(10) if you actually look at a rectangle with a diagonal with those endpoints.

Yeah it's weird. So would it still make a right angle if the width is root10? nope. then we'd have to calculate the angles of each corner in the triangle, and use the sin law to figure out the length.

throw this question in the garbage. waste of your time.

 

[FROGGBUSTER]

the dimensions of the rectangle are 5x7 aren't they? where is this sqrt(10) coming from?

 

[herkulease]

You're being tested two things. Pythagorean theorem and distance formula between two points. If you know how to do those then you're set.

If you "throw out" pure on well if I graph this thing it isn't gonna work or look nice then why bother. Dr. Romano is probably like the test writers. they think up what they want to test you then work backwards. Isn't it gonna work out perfect each and every time? No. You're gonna screw yourself over during the test getting hung up on questions when its obvious what they are looking for but the wording is kinda messed up.

Yes I realize that its messed up that the answer choices has 5 and 7 in them.

 

[AlbinoPolarBear]

You're being tested two things. Pythagorean theorem and distance formula between two points. If you know how to do those then you're set.

If you "throw out" pure on well if I graph this thing it isn't gonna work or look nice then why bother. Dr. Romano is probably like the test writers. they think up what they want to test you then work backwards. Isn't it gonna work out perfect each and every time? No. You're gonna screw yourself over during the test getting hung up on questions when its obvious what they are looking for but the wording is kinda messed up.

All of the questions will be screened to eliminate vague questions before they are added to the DAT. Having an entire question voided due to it not making sense will cause some headaches for the administrators of the DAT.

Dr. Romano is one guy who made a mistake. A question like this which doesn't obey the laws of mathematics will never ever make it past the screening process (i'm sure more than 1 person).

 

[herkulease]

All of the questions will be screened to eliminate vague questions before they are added to the DAT. Having an entire question voided due to it not making sense will cause some headaches for the administrators of the DAT.

Dr. Romano is one guy who made a mistake. A question like this which doesn't obey the laws of mathematics will never ever make it past the screening process (i'm sure more than 1 person).

My point is understand what is being asked of you and how to do the problem. If you get the same problem but with the numbers adjusted to make it all work out, you still know how to do them.

yes, Dr. Romano is 1 person so its easier for him to overlook things.

BUT the ada is not perfect. questions get vetted but mistakes slip through. If I could I would've taken a picture of chemistry question of mine asking to why something occurs. 3 of the choices were obviously wrong. I was left with two.

Only problem was compared identical things. as I noted in my breakdown its like telling some alaska is colder than alaska for one choice, in the 2nd choice alaska is warmer than alaska.

 

[HannibalLecter]

Yes I know what Dr. Romano is trying to do in this problem which is to state that hey the diagonal of a rectangle is this and this. But as you can see in my first post I was trying to see if there would be a faster way which there is if you were to take the ratios. The problem arises when you are given wrong variables. Two methods on the DAT should give you the same result. The timing is the issue and thats what I was trying to beat with my strategy. But obviously since the question itself doesn't have congruency in itself, it is worthless utilizing two different strategies.

Orgoman is very picky in what kind of strategy he wants you to use but he forgets that not every problem is going to be graphed up like he always does for you which is not how real life works.

As for the real DAT if you feel like the question/answer choices were wrong in any way you do have the option of asking the ADA to look in it for you. Why do you think there are test corrections do you think the actual DAT people take the test or people like you and me call them up demanding them to look it up. If you feel uncomfortable with a question and the answer choices you should make a note of it and report it accordingly. Just kind of sitting and letting it slide is not a proactive way of dealing with the most important test of your life.

 

[rockclock]

there's no mistake in the problem...the sides of the rectangle aren't parallel to the axes.

(sqrt(10))^2 + L^2 = (sqrt(25+49))^2
10 + L^2 = 74
L = 8

 

[HannibalLecter]

there's no mistake in the problem...the sides of the rectangle aren't parallel to the axes.

(sqrt(10))^2 + L^2 = (sqrt(25+49))^2
10 + L^2 = 74
L = 8

Check yo sources rockclock, I think your timing may be off

 

[rockclock]

Hahaha I was just drawing a picture to show you but this is A VERY POORLY worded problem. Because the width of the rectangle can never be sqrt(10) if you actually look at a rectangle with a diagonal with those endpoints.

...guess it's pretty standard at Cal to assume everyone and everything else, including the question itself, is wrong before realizing you are.

 

[PhansterZ]

Thought the same thing as everyone else.

You're my hero rock clock.

 

[FROGGBUSTER]

Thought the same thing as everyone else.

You're my hero rock clock.

are you the guy who keeps sucking rc's cock?

 

[PhansterZ]

...

 

[HannibalLecter]

My bad. Ok I stand corrected and I just didn't see it. Thank you for clearing it up for me. But there is no need of making fun of other people Phansterz. I was just in disagreement with rockclock.

And, why do you think I posted the question? I wanted an explanation for why I was wrong to begin with. Look at my OP.

 

[FROGGBUSTER]

...

my bad dude, i think i confused you with someone else.