I need some help with this problem. The perimeter of a rectangle is 62 meters. I

Question

I need some help with this problem. The perimeter of a rectangle is 62 meters. If the width wasdoubled and the length was increased by 21 meters, the perimeterwould be 120 meters. What are the length and width of the originalrectangle? Thank you for helping. I need some help with this problem. The perimeter of a rectangle is 62 meters. If the width wasdoubled and the length was increased by 21 meters, the perimeterwould be 120 meters. What are the length and width of the originalrectangle? The perimeter of a rectangle is 62 meters. If the width wasdoubled and the length was increased by 21 meters, the perimeterwould be 120 meters. What are the length and width of the originalrectangle? Thank you for helping.

Explanation / Answer

The perimeter of a rectangle is 62 meters.
2L + 2W = 62      divide across by2 1) L + W =31 If the width was doubled (2W) and the length wasincreased by 21 meters (L+21) , the perimeter would be 120meters. 2(L+21) + 2 (2W) = 120 2L + 42 + 4W =120           subtract 42 from each side 2L   + 4W =78       divide across by 2 tosimplify 2) L + 2W =39 1) L + W = 31 multiply 1) by -1 and add to 20 -L - W =-31 L + 2W =39       W =8           
L + W = 31 so L + 8 = 31 soL = 23
check 2L + 2W = 62          2(23) + 2(8) = 62           46 + 16 = 62 What are the length and width of the original rectangle?

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