the preimiter of the rectangular playing field is 406 yards. the length of the field is 7 yards less than quadruple the width, what are the demension of the playing field.

Answer 1

Perimeter = 406

Length = 4w - 7 (7 yds less than quadruple the width)

Width = w

P = 2(L+W)

406 = 2(4w - 7 + w)

406 = 2(5w - 7)

406 = 10w - 14

406 + 14 = 10w

420 = 10w

42 = w

now substitute 42 for w in the expression 4w-7 to find the length:

L = 4(42) - 7

L = 168 - 7

L = 161

Check to make sure dimensions add up to perimeter of 406

P = 2(161 + 42)

P = 2(203)

P - 406

Dimensions are Length = 161, Width = 42