The dimension of a rectangle solid are whole numbers. The area of the faces are 42cm square, 48cm square, and 56cm square. What are the dimensions of the solid?
2006-09-18 13:45:09 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
let x be the one side
y be the 2nd side
z be the 3rd side
1. xy = 42
2. xz = 48
3. yz = 56
from eq 1, x = 42/y and eq 3, z = 56/y
substitute to eq 2
xz = 48
(42/y)(56/y) = 48
2352 = 48y^2
y^2 = 49
y = 7 cm
x = 42/7 = 6 cm
z = 56/7 = 8 cm
goodluck ^_^
2006-09-18 13:50:42 · answer #1 · answered by ettezzil 5 · 1⤊ 0⤋
ettezil got it. I did it basically the same way. But I would say first draw a rectangle and name each side, so it helps you visualize. The area of each face is given by multiplying 2 sides, giving you the following equations
1. yz= 56
2. xz= 48
3. xy= 42 from there pick any of the equations and substitute. For ex from equation 1, you can say y=56/z and then replace/substitute the y in equation 3, and keep substituting until you get a number and then go back to the other equations and replace with that number. You should end up with 6, 7, and 8 as the answers. But you need to have the basics in math to be able to do the substitutions correctly. If you do, you should be able to get it right. If not, you should seek tutoring.
2006-09-18 21:16:33 · answer #2 · answered by Smarties 3 · 0⤊ 0⤋
48 = 6 * 8
42 = 6 * 7
56 = 7 * 8
The dimensions are 6, 7, and 8
here is how to figure it out
xy = 42
yz = 48
xz = 56
2006-09-19 01:27:23 · answer #3 · answered by Sherman81 6 · 0⤊ 0⤋
the sides lengths are 6 cm, 7cm, and 8 cm.
2006-09-18 20:48:18 · answer #4 · answered by frankgrimes.rm 2 · 0⤊ 0⤋
Sorry. I'm good at math but even this question stumps me. Sorry!!! Good luck!
2006-09-18 20:47:24 · answer #5 · answered by wmnofyourdreams 1 · 0⤊ 0⤋