the width of a rectangle is fixed at 4cm. Determine in terms of an inequality those lengths for which the area will be less than 92cm^2

the length must be less than ? cm

the solution is {L|L< ? cm

4 * L < 92

Divide both sides by 4.

To determine the lengths for which the area of the rectangle will be less than 92cm^2, we need to use the formula for the area of a rectangle, which is length × width.

Given that the width is fixed at 4cm, we can substitute this value into the formula:

Area = length × 4

We need to find the lengths for which the area is less than 92cm^2, so we can write this as an inequality:

Length × 4 < 92

Now, we need to isolate the length term by dividing both sides of the inequality by 4:

Length < 92 / 4

Simplifying the right side gives:

Length < 23

Therefore, the length must be less than 23 cm.

In interval notation, the solution is { L | L < 23 cm }.

To determine the lengths for which the area of a rectangle will be less than 92cm^2, we need to use the formula for the area of a rectangle:

Area = Length x Width

We know that the width is fixed at 4cm. Let's use the variable L to represent the length of the rectangle. So, the area in terms of L becomes:

Area = L x 4

According to the problem, the area must be less than 92cm^2. Therefore, we can write the inequality as follows:

L x 4 < 92

To solve for L, we can divide both sides of the inequality by 4:

L < 92/4

Simplifying, we have:

L < 23

So, the length must be less than 23cm.

To express the solution set in set-builder notation, we write:

{L | L < 23 cm}