Answer:
3 measurements of different rectangular prisms that each have a surface area
of 20 square units is given as
(4.5 × 1 × 1)
(2 × 1 × 2.67)
(2 × 3 × 0.80)
Explanation:
A rectangular prism is a cuboid and the surface area of a cuboid with length, x, width, y and height, z, is given as
S = 2xy + 2yz + 2xz
S = 2[xy + yz + xz]
So, the question asks us to list 3 different measurements of a rectangular prism with surface area of 20 square units.
S = 2[xy + yz + xz] = 20
[xy + yz + xz] = 10
So, with a little of trial and error, we can vary the values of x, y and z to obtain 3 separate measurements that give a surface area of 20 square units.
[xy + yz + xz] = 10
Let x = 4.5, y = 1, z = 1
(4.5×1) + (1×1) + (4.5×1) = 10, works!!!
(x, y, z) = (4.5, 1, 1)
[xy + yz + xz] = 10
Again, we can fix arbitrary values for two sides and calculate for the last side.
If x = 2 units, y = 1 unit,
(2×1) + (1×z) + (2×z) = 10
2 + 3z = 10
3z = 8
z = (8/3) = 2.667 units
(x, y, z) = (2, 1, 2.67)
[xy + yz + xz] = 10
And lastly, if x = 2, y = 3
(2×3) + (3×z) + (2×z) = 10
6 + 5z = 10
5z = 4
z = (4/5) = 0.80 unit
(x, y, z) = (2, 3, 0.80)
Hope this Helps!!!