Question

Measured in meters, a rectangular room has length a and width b where 7.5 ≤ a ≤ 7.6 and 5.4 ≤ b ≤ 5.5. Can the room be used as a library that must have a minimum area of 40 square meters to fit all the books?

Yes or No?

PLEASE HELP ASAP!!!

Answer 1

Yes, the room can be used as a library with a minimum area of 40 square meters to fit all the books.

The maximum possible area for the room is:

A = ab = (7.6)(5.5)

The minimum area of the room that can fit all the books is 40 square meters, or 4000 square centimeters:

4000 = A cm² = ab cm²

Solving for a, we get
a = 4000/b cm

Plugging this expression into the inequality 7.5 ≤ a ≤ 7.6, we get:

4000/b (5.45cm) ≤ 7.6 cm ≤ 4000/b (5.55cm)

Solving for b, we get
b = 10.8cm to 11.1cm

So we see that the room has a width of at least 10.8cm, which means that the room can definitely be used as a library with a minimum area of 40 square meters to fit all the books.

Answer 2

Yes

Explanation:

You want to know if a room with length in [7.5, 7.6] meters and width in [5.4, 5.5] meters can be used as a library requiring a minimum area of 40 square meters.

Area

The smallest area the room can have is the product of the shortest dimensions:

(7.5 m)(5.4 m) = 40.5 m²

The area of the room is at least 40.5 m², so can be used for the library (yes).

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