SOLUTION: A rectangular field is 4 times as long as it is wide. Let the width be x and the length 4x. If the length is decreased by 10 in. and the width increased by 2 in. the perimeter will
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-> SOLUTION: A rectangular field is 4 times as long as it is wide. Let the width be x and the length 4x. If the length is decreased by 10 in. and the width increased by 2 in. the perimeter will
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Question 175223: A rectangular field is 4 times as long as it is wide. Let the width be x and the length 4x. If the length is decreased by 10 in. and the width increased by 2 in. the perimeter will be 80 in. Find the dimensions of the original field. Answer by EMStelley(208) (Show Source):
You can put this solution on YOUR website! Note that you need to create new expressions using the information in the problem. "If the length is decreased by 10 in." is equivalent to saying 4x-10 since 4x represents the length. "and the width is increased by 2 in." is equivalent to saying x+2 since x represents the original width. Then, using the perimeter formula of P = 2W + 2L, we get that
80 = 2(x+2) + 2(4x-10)
Distributing:
80 = 2x + 4 + 8x - 20
Simplifying:
80 = 10x -16
Add 16 to both sides:
96 = 10x
Divide both sides by 10:
9.6 in = x
Thus the original width was 9.6 in and the original length was 4(9.6) = 38.4 in.
