Heigh, Width, and Length of a rectanglular prism are in the ratio 1:2:4.?

Question

The height, width, and length of a rectangular prism are in the ratio 1:2:4. If the surface area of the prism is 17,500cm^2, write an equation to model the problem and find the dimensions (height, width, and length) of the prism.If you can solve it please show all of your work and explain to me how you solved it step by step.

Answer 1

Let be a,b,c ,the height,width and length of the prism.
Let be A=17,500 the surface area of the prism wich has the formule:A=2(ab+bc+ac)
{a,b,c} are in the ratio{1,2,4} then a/1=b/2=c/4=k.Then we have a=k,b=2k,c=4k and we insert to the formule area.Then we have
A=2(2k^2+8k^2+4k^2)
A=28k^2, but A=17,500,then 28k^2=17,500, and k^2=625 =>k=25
a=k=25, b=2k=50, c=4k=100 is heigh, width and length of prism. OK?

Answer 2

If we let x = the height of the prism, and the ratio is given as 1:2:4, then

x = height
2x = width
4x = length

The surface area of the rectangular prism is given by:

A = (area of each face)

Since this is a rectangular prism, the faces opposite to each other have the same area, so

A = (top and bottom) + (front and back) + (left and right)

The top and bottom have area = width x length.
The front and back have area width x height.
The left and right faces have area length x height.

A = 2WL + 2WH + 2LH

But we know that H = x, W = 2x, L = 4x, so

A = 2(2x)(4x) + 2(2x)(x) + 2(4x)(x)
A = 16x^2 + 4x^2 + 8x^2
A = 28x^2

Since we're given that the surface area of the prism is 17500, then

17500 = 28x^2

Divide both sides by 28, to get

625 = x^2

To which x = +/- 25 (or, "plus or minus 25").
We reject the negative solution since x, the height, can't be expressed as a negative value, therefore x = 25.

Thus, the height is x = 25 cm
The width is 2x = 2(25) = 50 cm
The length is 4x = 4(25) = 100 cm

Answer 3

Basically there are 6 faces for this rectangular prism.
There are 2 pair of faces with surface area ( height x width) -----------(1)
There are another 2 pair of faces with surface area ( width x length)-(2)
The other 2pair of faces are having the surface area (height x length)-(3)
Assume that the Height is L cm
Than width is 2L cm
And the length is 4 Lcm
The first 2 pair of face's area is 2 ( Lx 2L)
The second 2 pair of face's area is 2 ( 2Lx 4L)
The third 2 pair of face's area is 2 ( Lx 4L)
So the total surface area is A= 2 ( Lx 2L) + 2 ( 2Lx 4L) + 2 ( Lx 4L)
That is A= 4 L^2 + 16 L^2 + 8 L^2
A = 28 L^2 -------------i
Given that the surface area is A= 17500 cm2-----ii

From i and ii ,
28 L^2 = 17500 cm2
L^2 = 625 cm2
that is L = 25 cm.
So Height = 25 cm
Width = 50 cm ( that is 2x 25cm)
Length = 100 cm ( that is 4x 25 cm)
Is it clear now my dear friend?

Answer 4

Assuming a rectangular prism:- V = 5 x 4 x 3 cm³ V = 60 cm³

Answer 5

Let

Length = l = 4x
Width = w = 2x
Height = h = x

Surface Area = s

s = 2lw + 2lh + 2wh = 2[lw + lh + wh]
= 2[4x*2x + 4x*x + 2x*x] = 2[8x^2 + 4x^2 + 2x^2]
= 2(14x^2) = 28x^2 = 17,500 cm^2

x^2 = 17,500/28 = 625
x = 25

Length = l = 4x = 4*25 = 100 cm
Width = w = 2x = 2*25 = 50 cm
Height = h = x = 25 cm

Answer 6

l : b : h = 1 : 2 : 4
Let l = x, b = 2x and h = 4x
Surface area = 2(lb + bh + hl) = 2 (2x^2 + 8x^2 + 4x^2) = 28x^2
So, 28x^2 = 17500
x = 25
So, length = 25 cm, breadth = 50 cm and height = 100 cm

Answer 7

A = 2(HW +LW+LH) = 17,500 cm^2
W = 2H
L = 4H
2(2H*H + 2H*4H + 4H*H) = 17,500 cm^2
H^2(2 + 8 + 4) = 8,750cm^2
14H^2 = 8,750cm^2
H^2 = 625 cm^2
H = √(625 cm^2)
H = 25 cm
W = 50 cm
L = 100 cm

Answer 8

the answer is 2.