Different approaches in Math

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1

<p>I always like to look at different approaches that people take to solve the same math problem. Can you think of any other way to solve this?</p>

<p>The areas of 3 faces of a rectangular solid are 72, 108, and 216. Find its dimensions.</p>

<p>My approach:</p>

<p>LW = 72
WH = 108
HL = 216</p>

<p>L = 72/W
H = 108/W</p>

<p>(72/W)(108/W) = 216;
(72*108)/216 = W^2;
36 = W^2;
W = 6
L = 12
H = 18</p>

<p>Another approach:
72 = 1<em>72, 2</em>36, 4<em>18, 6</em>12, 9<em>8
108 = 1</em>108, 2<em>54, 3</em>36, 4<em>27, 6</em>18, 9<em>12
216 = 1</em>216, 2<em>108, 3</em>72, 4<em>54, 6</em>36, 8<em>27, 9</em>24, 12*18</p>

<p>I realize that I can do something with factors of the areas. Are there any other ways of approaching this problem??</p>

2

<p>Well, it does help you visualize the shared sides. I did the problem the same way you did; LW=72, WH=108 … and I think that’s a pretty efficient way.</p>

3

<p>I think the most time friendly approach would be the first, JeffreyJung. There’s no need to explore other methods.</p>

4

<p>

Aww… why do you hate me… lol
I just find different approaches interesting… :)</p>

5

<p>Could you look at the provided solutions and just see if they fit? Just multiply out each possible pair of the 3 given dimensions.</p>

6

<p>

</p>

<p>What if this was one of the grid in problems asking for the volume of the rectangular solid?</p>

7

<p>Then I’m not sure. You may have to use one of the methods given.</p>