SOLUTION: The length of a rectangular playing field is 5ft less than twice its width.If the perimeter of the playing field is 230ft find the length and width of the field.

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Question 117653: The length of a rectangular playing field is 5ft less than twice its width.If the perimeter of the playing field is 230ft find the length and width of the field.
Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the perimeter of a rectangle is
P+=+2w+%2B+2l where l = length
and w = width
230+=+2w+%2B+2l
also given is
l+=+2w+-+5
2w+=+l+%2B+5
substitue 2w into 1st equation
230+=+l+%2B+5+%2B+2l
3l+=+225
l+=+75 ft answer
l+=+2w+-+5
75+=+2w+-+5
2w+=+80
w+=+40 ft answer
The length is 75 ft and the width is 40 ft
check answer
P+=+2w+%2B+2l
P+=+2%2A40+%2B+2%2A75
P+=+80+%2B+150
P+=+230
OK
l+=+2w+-+5
75+=+2%2A40+-+5
75+=+80+-+5
75+=+75
OK

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Given:
The length L is 5ft+ less than twice its widthW :
L+%2B+5ft+=+2W………=>…. +%28L+%2B+5ft%29%2F2+=+W………
the perimeter P+=+230ft+
P+=+2%28L%2BW%29
230ft+=+2%28L%2B%28L+%2B+5ft%29%2F2%29
230ft+=+2%28L%2BL%2F2+%2B+5ft%2F2%29

230ft+=+2L%2B+2L%2F2+%2B+2%2A5ft%2F2
230ft+=+2L%2B+L+%2B+5ft
230ft+=+3L+%2B+5ft
230ft+%96+5ft+=+3L+
225ft++=+3L+
225ft+%2F3+=+3L%2F3+
75ft+=+L+
+%28L+%2B+5ft%29%2F2+=+W………
+%2875ft+%2B+5ft%29%2F2+=+W
+80ft+%2F2+=+W
+40ft++=+W

Check:
P+=+2%28L%2BW%29
230ft+=+2%28+75ft+%2B+40ft%29
230ft+=+2%2A115ft
230ft+=+230ft