Asked by Josh
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!!
thanks!!
Answers
Answered by
Damon
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.
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.
Answered by
Damon
Whoh !
The bottom one is 4(x+2)^2 -x^2
Not 5 because bottom surface is on desk
The bottom one is 4(x+2)^2 -x^2
Not 5 because bottom surface is on desk
Answered by
Damon
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
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
Answered by
Damon
whoops second one wrong too
exposed area of second one = 5 x^2 - (x-2)^2 - (x+2)^2
exposed area of second one = 5 x^2 - (x-2)^2 - (x+2)^2
Answered by
Usha.S
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 :)
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 :)
Answered by
Krishnamurthy
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 - 2ã971) = -5.5747
x = 1/11(1 + 2ã971) = 5.7565
The lengths of the sides of
the cubes are 3.76, 5.76 and 7.76.
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 - 2ã971) = -5.5747
x = 1/11(1 + 2ã971) = 5.7565
The lengths of the sides of
the cubes are 3.76, 5.76 and 7.76.
Answered by
Muffin
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
[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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.