the perimeter of a rectangle is 44 m. If the width were doubled and the length were increased by 8 m, the perimeter would be 76 m. What is the length of the rectangle
Let us assume the length of the first rectangle = x meter let us assume the width of the first rectangle = y meter Perimeter of the first rectangle = 44 meter we already know Perimeter of a rectangle = 2 (Length + Width) Then in the case of the first rectangle we get 44 = 2(x + y) 44/2 = x + y x + y = 22 y = 22 - x Now coming to the case of the second rectangle The length of the second rectangle = x + 8 The width of the second rectangle = 2y Perimeter of the second rectangle = 76 meter then 76 = 2[(x + 8) + 2y] 76/2 = x + 8 + 2y 38 = x + 2y + 8 x + 2y = 38 - 8 x + 2y = 30 Now we replace the value of y that we found from the first equation. Then x + 2(22 - x) = 30 x - 2x + 44 = 30 -x = 30 - 44 -x = -14 x = 14 So the length of the first rectangle is 14 meters.
