1. You want to carpet a square room with an area of 350 square meters. You have a carpet that measures 5√14 by 3√14 meters. What is the length of the carpet to be added in able to fulfill the room?

Thank You!!

Since the room is square, its side is √350

= 5√14 m

your carpet is only 5√14 by 3√14
So clearly you will need an extra 2√14 m

To find the length of the carpet needed to cover the square room, we need to first calculate the side length of the room.

Given that the area of the square room is 350 square meters, we can use the formula for the area of a square, which is side length squared. Let's call the side length of the square room "s".

s^2 = 350

To find the value of "s", take the square root of both sides of the equation:

s = √350

Now, let's determine the length of the carpet that is already available.

The given carpet measures 5√14 by 3√14 meters. Since it is a square room, both the length and the width of the carpet are the same.

Let's assume the length of the carpet is L meters.

To fulfill the square room, the length of the carpet should be equal to or larger than the side length of the room (s). Therefore, we have the inequality:

L ≥ s

Substituting the value of "s" that we found earlier:

L ≥ √350

Finally, to find the minimum length of the carpet needed, we can calculate the square root of 350 and round it up to the nearest whole number.

L ≥ √350 ≈ 18.71 (rounded up to 19)

Therefore, the length of the carpet to be added should be at least 19 meters in order to fulfill the room.