a living room measure 450 x 330cm. find the dimension of the largest square tile that can be used to tile the floor without cutting
Area of the living room is 450 x 330 = 148500 cm^2.
Area of square = a x a
148500 = a^2
a = sq rt (148500) = 385.36 cm
the dimensions of the largest sq tile is 385.36 x 385.36 cm
148,502,3296
To find the dimension of the largest square tile that can be used to tile the floor without cutting, we need to find the greatest common divisor (GCD) of the width and length of the living room.
The width of the living room is 450 cm, and the length is 330 cm.
Let's calculate the GCD:
1. Find the prime factors of both numbers:
The prime factors of 450 are 2 * 3^2 * 5^2.
The prime factors of 330 are 2 * 3 * 5 * 11.
2. Determine the common prime factors:
The common prime factors are 2 * 3 * 5.
3. Multiply the common prime factors:
2 * 3 * 5 = 30.
Therefore, the GCD of 450 and 330 is 30.
This means that the largest square tile that can be used to tile the floor without cutting is 30 cm by 30 cm.
To find the dimension of the largest square tile that can be used to tile the floor without cutting, we need to find the greatest common divisor (GCD) of the room's length and width.
Step 1: Find the GCD
Using the given dimensions of the living room (450 x 330cm), we can find the GCD by applying the Euclidean algorithm.
Let's set up the equation:
GCD(450, 330) = GCD(330, 450 mod 330)
Calculating the remainder:
GCD(450, 330) = GCD(330, 120)
Continuing with the Euclidean algorithm:
GCD(330, 120) = GCD(120, 330 mod 120)
GCD(330, 120) = GCD(120, 90)
One more step:
GCD(120, 90) = GCD(90, 120 mod 90)
GCD(120, 90) = GCD(90, 30)
Final step:
GCD(90, 30) = GCD(30, 90 mod 30)
GCD(90, 30) = GCD(30, 0)
Since we have reached a remainder of 0, the GCD is the divisor from the previous step, which is 30.
Step 2: Determine the dimension of the largest square tile
The GCD represents the greatest square that can evenly fit into both the length and width without any leftover space. In this case, the GCD is 30.
Therefore, the largest square tile that can be used to tile the floor without cutting is a tile with dimensions of 30cm x 30cm.