Question

List the measurements of three different rectangular prisms that each have a surface area

Answer 1

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)

Step-by-step 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!!!