Question 106502: The edges of three cubes are consecutive odd integers. If the cubes are stacked as shown the total exposed surface area is 381 cm2. Find the lengths of the sides of the cubes.
i need an equation for this pls..
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The edges of three cubes are consecutive odd integers. If the cubes are stacked as shown the total exposed surface area is 381 cm2. Find the lengths of the sides of the cubes.
:
The areas of the 3 cubes would be:
ax^2 + b(x+2)^2 + c(x+4)^2 = 381
where and a,b,c are the number of sides of that cube that are exposed
:
An example,
x cube had two sides exposed
(x+2) had two sides exposed
(x+4) had one side exposed
:
2x^2 + 2(x + 2)^2 + 1(x + 4)^2 = 381
:
2x^2 + 2(x^2 + 4x + 4) + (x^2 + 8x + 16) = 381
:
2x^2 + 2x^2 + 8x + 8 + x^2 + 8x + 16 = 381
:
2x^2 + 2x^2 + x^2 + 8x + 8x + 8 + 16 = 381
:
5x^2 + 16x + 24 - 381 = 0
:
5x^2 + 16x - 357 = 0
Factors to:
(5x + 51)(x - 7) = 0
Only the positive solution wanted here:
x = +7
:
Nos. 7, 9, 11 would satisfy this situation:
2(7^2) + 2(9^2) + 11^2 = 381
:
Your problem may be different, but this method should help
|
|
|
