Question

A rectangular room must have a perimeter of 20 feet and an area of at least 20 square feet. Describe the possible widths of the room. Round your answers to the nearest tenth of a foot.

Answer 1

To find the possible widths of the room, we use the given perimeter and area information. The possible widths are approximately 3.4 feet and 6.6 feet.

Step-by-step explanation:

To find the possible widths of the room, we need to use the given perimeter and area information. Let's assume the length of the room is L and the width is W.

Perimeter of a rectangle = 2(L + W)

Given that the perimeter is 20 feet, we can solve for L + W = 10. Rearranging the equation, we get L = 10 - W.

Area of a rectangle = Length x Width

Given that the area is at least 20 square feet, we can set up the inequality L x W ≥ 20. Substituting the value of L from the previous equation, we have (10 - W) x W ≥ 20.

Simplifying this inequality, we get W2 - 10W + 20 ≥ 0. To solve for W, we can either use the quadratic formula or graph the inequality to find the possible values. In this case, the possible widths are approximately 3.4 feet and 6.6 feet.

Answer 2

Step-by-step explanation:

A rectangular room must have a perimeter of 20 feet and an area of at least 20 square feet. Describe the possible widths of the room. Round your answers to the nearest tenth of a foot

------------

L + W = 10 --> W = 10 - L

---

L*W >= 20

----

Solve L*W = 20

L*(10 - L) = 20

-L^2 + 10L - 20 = 0