SOLUTION: A rectangle has a perimeter of 62 cm. If the length and width are each increased by 2,by how many square centimeters does the area increase?
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Question 537777: A rectangle has a perimeter of 62 cm. If the length and width are each increased by 2,by how many square centimeters does the area increase? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! A rectangle has a perimeter of 62 cm.
2L + 2W = 62
Simplify, divide by 2
L + W = 31
W = (31-L); use this form for substitution
Find the original area (a):
a = LW
:
If the length and width are each increased by 2, by how many square centimeters does the area increase?
Find the new area (A):
A = (L+2)(W+2)
FOIL
A = LW + 2L + 2W + 4
:
Diff in area(D) = New area (A) - original area (a)
D = (LW + 2L + 2W + 4) - LW
D = LW - LW + 2L + 2W + 4
LW's cancel
D = 2L + 2W + 4
Replace W with (31-L)
D = 2L + 2(31-L) + 4
D = 2L + 62 - 2L + 4
D = 2L - 2L + 62 + 4
2L's cancel
D = 62 + 4
D = 66 sq/cm increase
