Given that a rectangle with length 3x inches and width x + 5 inches has the property that its area and perimeter have equal values, what is X?
+312 Area = 3X(X + 5) = 3X^2 + 15X
Perimeter = 2(3X) + 2(X + 5) = 6X + 2X + 10 = 8X + 10
3X^2 + 15X = 8X + 10
3X^2 + 7X - 10 = 0
3X^2 - 3X + 10X - 10 = 0
3X(X-1)+10(X-1) = 0
(3X + 10)(X -1) = 0
X = 1, X = -10/3
We only consider the positive solution in this case. X = 1
