Question

the edges of 3 cubes are consecutive odd intergers. if the cubes aer stacked on a desk as shown, the total exposed surface area is 381. find the lenths of the sides of the cubes

thanks!!

Answer 1

x-2
x
x+2

exposed area of first one = 5(x+2)^2 -x^2
exposed area of second one = 5 x^2 - (x-2)^2
exposed area of top one = 5 (x-2)^2
so
5(x^2+4x+4)-x^2+5x^2-x^2+4x-4+5(x^2-4x+4)=381

(5-1+5-1+5)x^2+(20+4-20)x+(20-4+20)=381
13x^2+4x-4 = 381
13x^2 +4x - 385 = 0
x = [ -4+/-sqrt(16+20020)/26
x = [-4+/-138]/26
136/26 = 5.44
well so I would get like 3,5,7
but suspect I have an arithmetic error.
however that is a method.

Answer 2

Whoh !

The bottom one is 4(x+2)^2 -x^2

Not 5 because bottom surface is on desk

Answer 3

x-2
x
x+2

exposed area of first one = 4(x+2)^2 -x^2
exposed area of second one = 5 x^2 - (x-2)^2
exposed area of top one = 5 (x-2)^2
so
4(x^2+4x+4)-x^2+5x^2-x^2+4x-4+5(x^2-4x+4)=381

(4-1+5-1+5)x^2+(16+4-20)x+(16-4+20)=381
12x^2 +32 = 381
12x^2 =349
x^2 = 29.08
x = 5.4
well, not much change, probably still have an error

Answer 4

whoops second one wrong too

exposed area of second one = 5 x^2 - (x-2)^2 - (x+2)^2

Answer 5

The equation should be:
Let x represent middle box, (x-2) represent top box and (x+2) represent side length of bottom box.
381=5(x+2)^2-(x)^2+5x^2-(x-2)^2+5(x-2)^2
then expand... and simplify to...
381=13x^2+4x+16
0=13x^2+4x-365
now use quad formula and x=5.14, (x-2) is 3.14 and (x+2) is 7.14

i'm pretty sure this is correct :)

Answer 6

The edges of three cubes are consecutive odd integers.
If the cubes are stacked on a desk,
the total exposed surface area is 381 cm^2.
Find the lengths of the sides of the cube.
(x - 2), x and (x + 2)
The exposed area of the first cube = 4(x + 2)^2 - x^2
The exposed area of the second cube = 5x^2 - (x - 2)^2 - (x + 2)^2
The exposed area of the top cube = 5 (x - 2)^2
The total exposed surface area:
4(x^2 + 4x + 4) - x^2 + 5x^2 - (x^2 - 4x + 4) - (x^2 + 2x + 4) + 5(x^2 - 4x + 4) = 381
11x^2 - 2x + 28 = 381
11x^2 - 2x - 353 = 0
x = 1/11(1 - 2ã971) = -5.5747
x = 1/11(1 + 2ã971) = 5.7565
The lengths of the sides of
the cubes are 3.76, 5.76 and 7.76.

Answer 7

Your exact equation would look like
[5(x+4)^2 - (x+2)^2] + [5(x+2)^2 - x^2] + 5x^2 = 381.

If you solve that through for x you will get your exact value of x, which is 3. From that you can find the other odd integers