The dimension of the rectangles are l = 2 cm, 9 cm and b = 9 cm, 2 cm.
What is a rectangle?
A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
Given that,
Area of rectangle A = l x w = 18 sq cm. .......(1)
perimeter of rectangle P = 2(l + w) = 22 cm ........(2)
Find length(l) and width (w)
Use equation (1) to solve for length (l) then substitute it into equation (2) to solve for width (w).
18 = l x w
l = 18/w
Substituting in equation (2)
2(18/w + w) = 22 cm.
18/w + w = 11
Multiple both sides of the equation by w
18 + [tex]w^{2}[/tex] = 11w
[tex]w^{2}[/tex] - 11w + 18 = 0
Now solve by factoring.
(w - 9)(w - 2) = 0
=> w = 9 cm or 2 cm
If w = 2 cm, l = 18/2 = 9 cm.
If w = 9 cm, l = 18/9 = 2 cm.
Hence, The dimension of the rectangles are l = 2 cm, 9 cm and b = 9 cm, 2 cm.
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