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A rectangle has length triple the side of this square and width two units less than the side of this square if the two areas are equal what are the squares dimensions?
Wiki User
∙ 12y ago
S = side of the square
S2 = area of the square
3S = length of the rectangle
S-2 = width of the rectangle
3S (S-2) = area of the rectangle
Since the areas are equal . . .
3S (S-2) = S2
Eliminate parentheses on the right side:
3S2 - 6S = S2
Subtract S2 from each side:
2S2 - 6S = 0
Factor the left side:
S (2S - 6) = 0
S = 0 is the trivial solution. The other, useful solution is
2S - 6 = 0
S - 3 = 0
S = 3
Check:
Square: Area = S2 = 9
Rectangle: Area = 3S (S-2) = 9 (1) = 9
The areas are equal. yay!
Wiki User
∙ 12y ago
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