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}