Calling all mathematicians!

Okay, I am having some problems with my Maths homework. I know there is another Maths thread already doing the rounds in GC, but I just figured the probability of getting a quick response may be slightly higher if I created a separate thread, bla bla bla, you get the picture! :p

Here are the two offending questions:

1. The sides of a rectangle are in the ratio 2:3. The diagonal is of length 26cm. Find the perimeter.

2. A cube has volume 10cm^3. Find the sum of the lengths of the edges, and the total surface area.

Oh, by the way. I already have the answers to these questions, as they are written on the back of the sheet. However, I don't know how to work the answer out. So if anyone can explain how to work it out, I'd really appreciate it.

(This may take a while to type, so someone might post before me)

1. OK, a rectangle with a diagonal is 2 congruent right triangles on top of one another, right? Lets call the sides of the triangle 2a and 3a (the ratio, 2 of something to 3 of something), which are also two of the sides of the rectangle, and the side opposite the right angle is 26cm, the diagonal. Simple Pythagorean Theorem, (2a)^2 + (3a)^2 = 26^2. Work it out, a=52, so the sides are 104cm and 156cm, and thus the perimeter is 520cm.

2. Ok, a cube has all the same sides. Volume of a cube = length times width times height. Since those are all the same, let's just call them all "a". So a^3 = 10cm^3. a = (cube root)(10)cm. There are 12 sides to a cube, so the sum of the lengths of the edges = 12(cube root)(10)cm. There are six sides to a cube. Each side of a cube is a square, and the area of a square = length times width, so the surface area of a cube = 6 times length time width. So surface area = 6a^2 = 6 x 10^(2/3)cm.

Dude i think she wanted that in english

Well if you posted the answer for number 1, I bet I could work out the answer and show you hjow I got it. Otherwise I've kinda forgotton how to do this :(

For #2, I CAN help you.

First, the vol of a cube is length times width times height right? But since all sides of a cube are equal, its just multiplying the same number 3 times.

So, 10 ^ 3 (which is really 1000) is just 10 times 10 times 10.

So, each side is 10 cm in length.

And since there's 12 edges on a cube, you just multiply 10 times 12 to get 120 cm, which is the total sum of the edges.

For SA, simply just find the area of one of the sides and multply it by 6, since theres 6 sides on a cube.

By finding the area of one side, you get 100 square cm (10 times 10)

So then you multply that by 6, and you end up with a total surface area of 600 cm squared.

I hope that made some sense to you, :)

Quote:

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Originally Posted by SeeDRankLou

(This may take a while to type, so someone might post before me)

1. OK, a rectangle with a diagonal is 2 congruent right triangles on top of one another, right? Lets call the sides of the triangle 2a and 3a (the ratio, 2 of something to 3 of something), which are also two of the sides of the rectangle, and the side opposite the right angle is 26cm, the diagonal. Simple Pythagorean Theorem, (2a)^2 + (3a)^2 = 26^2. Work it out, a=52, so the sides are 104cm and 156cm, and thus the perimeter is 520cm.

2. Ok, a cube has all the same sides. Volume of a cube = length times width times height. Since those are all the same, well just call them all "a". So a^3 = 10cm^3. a = (cube root)(10)cm. There are 12 sides to a cube, so the sum of the lengths of the edges = 12(cube root)(10)cm. There are six sides to a cube. Each side of a cube is a square, and the area of a square = length times width, so the surface area of a cube = 6 times length time width. So surface area = 6a^2 = 6 x 10^(2/3)cm.

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Grade: A

Quote:

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Originally Posted by GooeyToast

Well if you posted the answer for number 1, I bet I could work out the answer and show you hjow I got it. Otherwise I've kinda forgotton how to do this :(

For #2, I CAN help you.

First, the vol of a cube is length times width times height right? But since all sides of a cube are equal, its just multiplying the same number 3 times.

So, 10 ^ 3 (which is really 1000) is just 10 times 10 times 10.

So, each side is 10 cm in length.

And since there's 12 edges on a cube, you just multiply 10 times 12 to get 120 cm, which is the total sum of the edges.

For SA, simply just find the area of one of the sides and multply it by 6, since theres 6 sides on a cube.

By finding the area of one side, you get 100 square cm (10 times 10)

So then you multply that by 6, and you end up with a total surface area of 600 cm squared.

I hope that made some sense to you, :)

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Grade: E

Quote:

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Originally Posted by SeeDRankLou

1. Work it out, a=52, so the sides are 104cm and 156cm, and thus the perimeter is 520cm.

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Once you know a=52cm, the sides are 2a, 3a, 2a, and 3a, making the perimeter 10a=520cm. Same difference, but keeps the arithmetic simpler.

Thanks guys! :D

Just one more thing though. SRL, The answer you gave me for question 2 really helped me understand what to do, so thank you. However, for question 1, the answer sheet says "20(square root)(13)cm". Although, your answer must be correct because you really seem to know what you're doing. Is this merely another way of writing the answer? Or do you think it is just a mistake on the sheet?

Quote:

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Originally Posted by Endless

Grade: E

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To be fair, I think Gooey Toast misinterpreted the question. :)

Quote:

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Originally Posted by Cless

Thanks guys! :D

Just one more thing though. SRL, The answer you gave me for question 2 really helped me understand what to do, so thank you. However, for question 1, the answer sheet says "20(square root)(13)cm". Although, your answer must be correct because you really seem to know what you're doing. Is this merely another way of writing the answer? Or do you think it is just a mistake on the sheet?

Quote:

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Originally Posted by Endless

Grade: E

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To be fair, I think Gooey Toast misinterpreted the question. :)

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Yeah I smurfed up. Sorry. It seems my Algebra skills have been lost over the last 2 yrs. Hopefully Alg 2 will re-vamp them.

Quote:

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Originally Posted by Cless

Thanks guys! :D

Just one more thing though. SRL, The answer you gave me for question 2 really helped me understand what to do, so thank you. However, for question 1, the answer sheet says "20(square root)(13)cm". Although, your answer must be correct because you really seem to know what you're doing. Is this merely another way of writing the answer? Or do you think it is just a mistake on the sheet?

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OOOHHHH SSNNNAAAPPP!!!!

I was doing that a little fast, good eye. I said a=52. I was wrong, I missed a step.

(2a)^2 + (3a)^2 = 26^2
4a^2 + 9a^2 = 676
13a^2 = 676
a^2=52
a=(square root)(52)=2(square root)(13).

So the sides are 4(square root)(13)cm and 6(square root)(13)cm, which means the perimeter is 20(square root)(13)cm.

A lesson to all, always double check your math work. In hindsight, I wonder if there exists a rectangle with sides of 104cm and 156cm and a diagonal of 26cm. :tongue: Sorry :D

I got 72.11071767676787 for number one. =( I don't understand how the sides of the rectangle can be 104cm and 156cm if the diagonal is 26.

EDIT: I just read your post. Yeah, I got the same thing.

SRL saves the day yet again.

xD I did the same thing.

I have no idea, and I'm doing accounting in college, luckily I don't need to know that stuff so phew :D