Question

Describe the possible lengths of the third side of the triangle given that the lengths of the other two sides are 2 feet and 40 inches

Answer 1

The possible lengths of the third side of the triangle are any values greater than 5.33 feet.

Step-by-step explanation:

The possible lengths of the third side of a triangle can be determined by applying the triangle inequality theorem. According to this theorem, the sum of any two sides of a triangle must be greater than the length of the third side. In this case, the two given sides are 2 feet and 40 inches. To compare them, convert both lengths to the same unit—either feet or inches.

Since 1 foot is equal to 12 inches, the length of the second side in feet is 40 inches ÷ 12 = 3.33 feet (rounded to two decimal places).

Now, let's apply the triangle inequality theorem. The sum of the two given sides must be greater than the third side:

2 feet + 3.33 feet > Third side length

5.33 feet > Third side length

Therefore, the possible lengths of the third side of the triangle are any values greater than 5.33 feet.

Answer 2

The length of the third side is between 16 inches and 64 inches.

Step-by-step explanation:

The length of a side of a triangle is between the sum and the difference of the lengths of the other two sides.

First, we need both sides in the same units. Let's convert feet to inches.

2 ft * (12 in.)/(ft) = 24 in.

The sides measure 24 inches and 40 inches.

Now we add and subtract the two lengths.

40 in. + 24 in. = 64 in.

40 in. - 24 in. = 16 in.

The length of the third side is between 16 inches and 64 inches.