The width of a rectangle is fixed at 7cm. Determine (in terms of an inequality) those lenghts for which the area will be less than 161cm squared.
The length must be less than ? cm.
(simplify your answer)
The solution is {L l L < ? cm.}
(simplify your answer)
can someone please help guide me on this problem? thank you in advance
Calculate L for which L*W=161, and then construct the inequality or the set desired.
I got 7 x 23 = 161
so for the first answer
The length must be less than ? cm
what do I put there??
"The solution set is {L | L < 23 cm.} "
Would that do?
To solve this problem, we can use the formula for the area of a rectangle, which is length multiplied by width. In this case, the width is fixed at 7 cm.
Let's denote the length as L. We are given that the area should be less than 161 square centimeters.
The inequality for the area less than 161 cm^2 can be written as:
L * 7 < 161
To isolate L, we divide both sides of the inequality by 7:
L < 161 / 7
Simplifying the right side gives:
L < 23
Therefore, the length must be less than 23 cm.
In terms of an inequality, the solution is {L | L < 23 cm}. This means that the length can take any value less than 23 centimeters to ensure the area is less than 161 sq cm.