Area of rectagnle = (L) (W)
Area = (6cm) (4 cm)
Area = 24 cm²
If area is to be doubled, with equal length added to each dimension:
Let x = length added to each dimension
6 + x = length
4 + x = width
2 (24) = area doubled
Equation:
2 (24) = (6 + x) (4 + x)
48 = 24 + 6x + 4x + x²
Rewrite to standard form:
x² + 10x + 24-48 = 0
x² + 10x - 24 = 0
Factor:
(x - 2) (x + 12) = 0
x - 2 = 0 x + 12 = 0
x = 2 x = -12
Choose the positive root for distance, that is, x=2
Therefore, each dimension must be increased by 2 cms. to double the area from the original area given :-)
