The area of a rectangle is 30 square centimeters, and its perimeter is 22 centimeters.Find the dimensions of the rectangle.
A)22 cm by 22 cm
B)5 cm by 5 cm
C)5 cm by 6 cm
D)5 cm by 3 cm
E)3 cm by 6 cm

Question

Quizplus · Accepted Answer

Let the length and width of the rectangle be 'l' and 'w' respectively. Then we have:
lw = 30        ... (1)   (since area = lw)
2(l+w) = 22   ... (2)   (since perimeter = 2(l+w))
Simplifying equation (2), we get:
l+w = 11       ... (3)
Now we have two equations (1) and (3) in two variables 'l' and 'w'. We can solve for 'l' and 'w' by substitution or elimination. Here we use substitution:
From equation (3), we have:
l = 11-w
Substituting this into equation (1), we get:
(11-w)w = 30
Simplifying and solving for 'w', we get:
w^2 - 11w + 30 = 0
(w-5)(w-6) = 0
So, w = 5 or w = 6.
If w = 5, then l = 11-w = 6, which satisfies equation (1).
If w = 6, then l = 11-w = 5, which also satisfies equation (1).
Therefore, the dimensions of the rectangle are either 5 cm by 6 cm or 6 cm by 5 cm. However, since the question asks for "the" dimensions, we choose the option that is given first, i.e., 5 cm by 6 cm.

The Area of a Rectangle Is 30 Square Centimeters, and Its