The width of a rectangle is fixed at 19 cm. What lengths will make the perimeter greater than 82 cm. The length must be greater than ___ cm
The perimeter of a rectangle is given by P = 2(L + W). We want P > 82cm with width fixed at 19cm.
2(L + 19) > 82
Solve for L.
Start with perimeter = 2(W+L)
If W=19, and perimeter > 82, we end up with the inequality:
2(19+L) > 82
Solve for L to get the answer.
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To find the length that makes the perimeter of a rectangle greater than 82 cm, we need to understand the formula for the perimeter of a rectangle. The perimeter of a rectangle is calculated by adding the length of all its sides, which in this case would be adding the width twice and the length twice.
The formula for the perimeter of a rectangle is:
Perimeter = 2 × (Length + Width)
Given that the width is fixed at 19 cm, we can substitute the value into the formula:
Perimeter = 2 × (Length + 19)
Now, we need to solve the inequality where the perimeter is greater than 82 cm:
2 × (Length + 19) > 82
Let's simplify the equation:
Length + 19 > 41
Length > 41 - 19
Length > 22
Therefore, the length must be greater than 22 cm to make the perimeter of the rectangle greater than 82 cm.