Question

The perimeter of a rectangle is 110m , and the area of the rectangle is 54m^2 . Find the dimensions of the rectangle.

Answer 1

Any ideas?

Answer 2

You have two equations - one for area and one for perimeter. Then, if your sides are:

a = length
b = width
\[P=2a+2b\]and\[A=ab\]From your numbers, we get\[110=2a+2b\]and\[54=ab\]Choosing any one of the last two equations, we can solve for one of the variables and sub. it into the remaining equation, so\[54=ab \rightarrow b=\frac{54}{a}\]Substituting this into the perimeter equation,\[110=2a+2\frac{54}{a} \rightarrow 55=a+\frac{54}{a} \rightarrow 55a=a^2+54\]This is quadratic in a.\[a^2-55a+54=0\rightarrow a=\frac{-(-55){\pm}\sqrt{(-55)^2-4(1)(54)}}{2(1)}\]i.e.\[a=1,54\]
then \[b=54,1\] respectively.

Answer 3

So your length/width combinations are:

(a,b) = (1,54) or (54,1).