Can someone help me out with this Area question

Step-by-step explanation:

The area of a rectangle is the product of its length and width:

  A = 171 = bh

The perimeter of a rectangle is the sum of the lengths of its sides:

  P = 54 = b + h + b + h = 2(b +h)

We can use the latter equation to write an expression for h that can be substituted into the first equation.

  27 = b + h . . . . divide by 2

  h = 27 -b . . . . . subtract b

Now, the area is

  171 = b(27-b) = -b^2 +27b

Multiplying by -1 we get ...

  b^2 -27b = -171

adding the square of half of 27, we can "complete the square":

  b^2 -27b +13.5^2 = -171 +13.5^2 = 11.25

  (b -13.5)^2 = 11.25 . . . . write as a square

  b -13.5 = -√11.25 . . .  . . find the negative square root

  b = 13.5 -√11.25 ≈ 10.1459

  h = 27 -b ≈ 16.8541

The missing measurements are approximately ...

  b = 10.1459

  h = 16.8541

Comment on the problem

We suspect a typo in the problem. If the perimeter were 56, then the dimensions would be 9 and 19, integer factors of 171.