Mathematics
The length of a rectangle is twice the side of a square and its width is 6 cm greater than the side of the square. If area of the rectangle is three times the area of the square; find the dimensions of each.
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Answer
Given:
Let s be the side of the square.
Length of the rectangle = 2 x Side of the square
⇒ l = 2s
Width of the rectangle = Side of the square + 6
⇒ w = s + 6
Area of the rectangle = 3 x area of the square
⇒ l x w = 3s2
⇒ 2s x (s + 6) = 3s2
⇒ 2s2 + 12s = 3s2
⇒ 2s2 + 12s - 3s2 = 0
⇒ - s2 + 12s = 0
⇒ s2 - 12s = 0
⇒ s(s - 12) = 0
⇒ s = 0 or 12
Since the side cannot be zero, s = 12 cm.
The dimensions of the rectangle:
l = 2 x s = 2 x 12 cm = 24 cm
w = s + 6 = 12 + 6 = 18 cm
Hence, the length and width of the rectangle are 24 cm and 18 cm, and the side of the square is 12 cm.
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