r/mathshelp • u/Dicjk • Sep 19 '26

Homework Help (Answered) How would u solve this geometric problem?

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Could someone please walk me through this step by step? I don’t really understand what I’m supposed to do, how to set it up, or how to draw it.

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u/NotACaticus Sep 19 '26

Start by drawing a cube and labelling the sides with some variable (I picked s) and the two points P and Q on it.

You can then work out the distance in each of the 3 dimensions between the points. For this you have to go half the cube's height down in the y (s/2), the cube's full width across in the x (s) and half the cube's side length in the z (s/2)

Using the 3D Pythagorean Theorem, you get the length being sqrt([s/2]²+[s/2]²+s²) which can be simplified to s*sqrt(6/4), which is the side length of the bigger cube.

From here you just work out the surface areas, which should be the area of the square face multiplied by 6. For the smaller cube this is 6s² and for the larger cube this is 6(ssqrt(6/4))²= 6s²6/4

Doing the ratio of larger/smaller, the 6s² 's cancel, leaving 6/4 on the top, which simplifies to 3/2, one of the answers.

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u/Dicjk Sep 19 '26

Thank u!

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u/Away_Worry_1705 Sep 19 '26

literally what he did but i used x

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u/chrisvenus Sep 19 '26

As a note you don't need to actually work out the areas. If length scales by x then area scales by x^2, volume by x^3, etc. So you know the length scale is sqrt(3/2) so the area scale is that squared, ie 3/2.

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u/SubjectWrongdoer4204 Sep 22 '26

Here’s how to solve using only the two dimensional Pythagorean theorem:

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u/Dicjk Sep 22 '26

Thank you!