The width of a rectangle is fixed at 16cm. What lengths will make the perimeter greater than 84cm?
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Let
L=length,
W=width=16 cm,
From Perimeter = 2(L+W)
we need
2(L+W)>84 cm
Substitute W=16 cm
we get
2(L+16)>84
(L+16)>84/2
L+16>42
L>?
To find the lengths that will make the perimeter greater than 84cm, we need to understand the formula for calculating the perimeter of a rectangle. The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Width)
In this case, the width is fixed at 16cm. We want to find the lengths that will result in a perimeter greater than 84cm.
Let's substitute the values into the formula and solve for the length:
84cm < 2 * (Length + 16cm)
Divide both sides of the inequality by 2 to isolate the expression inside the parentheses:
42cm < Length + 16cm
Subtract 16cm from both sides of the inequality:
42cm - 16cm < Length
26cm < Length
Therefore, any length greater than 26cm will make the perimeter of the rectangle greater than 84cm.