Question

the perimeter of a rectangle is at least 100 inches, and the width must be less than double the length. the length must be over 15 inches long. which of the following inequalities correctly describes the perimeter? (1 point)

$2l + 15w \geq 100$

$l + w \geq 100$

$2l + 2w \geq 100$

$2l + 2w \leq 100$

Explanation:

Step1: Recall the formula for the perimeter of a rectangle

The formula for the perimeter \(P\) of a rectangle is \(P = 2L+2W\), where \(L\) is the length and \(W\) is the width.

Step2: Interpret the "at least" condition

The phrase "at least 100 inches" means that the perimeter \(P\) is greater than or equal to 100. Substituting \(P = 2L + 2W\) into the inequality, we get \(2L+2W\geq100\).

Answer:

\(2L + 2W\geq100\) (the third option)