Answered

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Lesson Component 4 (Lesson Activity)
Part 4A
Stem for Items 1 and 2
A set of storage spaces (Set A), in the shape of a rectangular prism, have a height of (2x-1) meters and a
volume of (6x³- 13x² + x + 2) cubic meters.
Another set of storage spaces (Set B), again in the shape of a rectangular prism, also have a height of
(2x-1) meters, with a base area of (3x² -7x-6) square meters.
A third set of storage spaces (Set C), also in the shape of a rectangular prism, have a height of (3x-2) meters
and a base area of (2x²+x-3) square meters.
​

Sagot :

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Item 1

Given the information provided:

- Set A: Rectangular prism with height (2x-1) meters and volume (6x³- 13x² + x + 2) cubic meters

- Set B: Rectangular prism with height (2x-1) meters and base area (3x² -7x-6) square meters

- Set C: Rectangular prism with height (3x-2) meters and base area (2x²+x-3) square meters

Determine the length and width of each set of storage spaces.

Solution for Item 1

To find the length and width of each set of storage spaces, we can use the formula for the volume and base area of a rectangular prism.

For Set A:

Volume = length × width × height

(6x³- 13x² + x + 2) = length × width × (2x-1)

Solving for the length and width:

Length × Width = (6x³- 13x² + x + 2) / (2x-1)

For Set B:

Base Area = length × width

(3x² -7x-6) = length × (2x-1)

Solving for the length and width:

Length = (3x² -7x-6) / (2x-1)

Width = (2x-1)

For Set C:

Base Area = length × width

(2x²+x-3) = length × (3x-2)

Solving for the length and width:

Length = (2x²+x-3) / (3x-2)

Width = (3x-2)

Therefore, the length and width of each set of storage spaces can be determined using the given information.

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