Question

The perimeter of a rectangle must be less than 170170 feet. If the length is known to be 4444 feet, find the range of possible widths for the rectangle. (Note: The formula for the perimeter of a rectangle is P=2l+2wP=2l+2w , where l is the length and w is the width). Express your answer in interval notation. Use decimal form for numerical values.

Answer 1

Answer:

$w \in (0,41)$

where w is width of rectangle.

Step-by-step explanation:

We are given the following in the question:

The perimeter of a rectangle must be less than 170 feet.

Length of rectangle = 44 feet

Perimeter of rectangle =

$2\times (\text{Length + Width})$

Let w be the width of rectangle.

According to the question,

$P < 170\\2(44 + w)<170\\44 + w < 85\\w < 41$

Thus, the width of triangle should be less than 41. Since w cannot take negative values, we can express value of w in interval notation as,

$w \in (0,41)$