Answer:
The area is a rational number.
Step-by-step explanation:
Consider the provided information.
A ballroom has a square dance floor. The area of the floor is 400 square feet.
Area of square = (side)²
Substitute the respective value in above formula.
400 = (side)²
√400 = side
20 feet = side
Ignore the negative value as side cannot be a negative number.
Now it is given that the length of each side of the square increased by one foot,
Thus, the new side is 20 + 1 = 21 feet
Now find the area of new square = (side)²
A = 21²
A = 21×21
A = 441 square feet
The number 441 is a rational number.
Hence, the area is a rational number.
We have that If the length of each side of the square increased by one foot,
Yes, Area will be a rational number
From the question we are told that
. The area of the floor is 400 square feet
the length of each side of the square increased by one foot,
Generally the equation for the Area of a square is mathematically given as
a=LxB
a=400
Rational Numbers
This simply means expressible as a ratio of whole numbers.
Therefore
If the length of each side of the square increased by one foot then the value will still be expressible as a ratio of whole numbers.
Hence
Yes, Area will be a rational number
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