the width of a rectangle is fixed at 12 cm. What lengths will make the perimeter greater than 98 cm.
Any length greater than 37 cm.
2*(37 + 12) = 98 is the perimeter if the length is 37 cm.
2W + 2L > 98.
2*12 + 2L > 98,
24 + 2L > 98,
2L > 98-24,
2L > 74,
L > 37.
To find the lengths that will make the perimeter greater than 98 cm, we first need to understand the formula for calculating the perimeter of a rectangle.
The formula for the perimeter (P) of a rectangle is given by:
P = 2L + 2W
where L represents the length of the rectangle and W represents the width.
In this case, as per the given information, the width is fixed at 12 cm. Thus, the equation becomes:
P = 2L + 2(12)
P = 2L + 24
Now, we want to find the lengths (L) that will make the perimeter greater than 98 cm. So, we can set up an inequality based on this condition:
2L + 24 > 98
To solve this inequality, we can subtract 24 from both sides:
2L > 74
Finally, we can isolate L by dividing both sides of the inequality by 2:
L > 37
Therefore, the lengths greater than 37 cm will make the perimeter of the rectangle greater than 98 cm.