Answer:
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
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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.
