A tile installer has selected four different size square tiles to cover a floor. The areas of the tiles are Tile A = 9 in.², Tile B = 25 in.², Tile C = 34 in.², and Tile D = 76 in.². For which tiles are the lengths of the sides rational?
ah, now I see why you asked the fence question
the length of the side of a square of area A is square root of A
sqrt 9 = 3 very rational
sqrt 25 = 5, again rational
sqrt 34 = nothing nice ! sqrt (2*17) yuuk
sqrt 76 = 2 sqrt (19) again not nice
To determine which tiles have rational side lengths, we need to find the square roots of the areas and check if they are rational numbers.
Let's find the square roots of each tile's area:
- Tile A: The square root of 9 in² is 3 in. This is a rational number because 3 can be expressed as a fraction 3/1.
- Tile B: The square root of 25 in² is 5 in. Again, this is a rational number because it can be expressed as 5/1.
- Tile C: The square root of 34 in² is approximately 5.83 in. This is an irrational number because it cannot be expressed as a fraction.
- Tile D: The square root of 76 in² is approximately 8.72 in. Like Tile C, this is an irrational number.
Hence, the tiles with rational side lengths are Tile A and Tile B.