Solve the following problems. Show step by step solutions

Question

3. If a floor area of a classroom is 5000 square inches,

a. how wide is the classroom in square meters?

b. How many square tiles with a side length of 100 cm can fit in its room?

Answer 1

Because 3.a) is a bit confusing, so I'll give the dimensions of the room in meters and give the area in square meters.

3.a) Firstly, we need to convert inches into meters which can be done by... 12in = 1ft, 3.28ft = 1 m

We're squaring each ratio because we have to make the units match so they may cancel out,

just like 2/2 = 1; The unit that we want should be in the numerator.

A = 5000 in² × (1ft / 12in)² × (1m / 3.28ft)²

= 5000in² × (1ft² / 144in² ) × (1m² / 10.7584ft² )

= (5000 × 1 × 1m²) / (1 × 144× 10.7584) = 3.23m²

3.b) Converting 3.23m² into square centimeters with conversion factor 1m = 100cm...

A = 3.23m² × (100cm / 1m)² = 3.23m² × 10000cm² / 1m² = 32300cm²

The area of the square tile with side length s = 100cm is A = s² = (100cm)² = 10000cm². This is obviously less than the room we have. Now, we need to see how many times can we multiply the area of the small tile to get the area of the room and we'll do that by this equation: n × 10000cm² = 32300cm²

We need n = 32300 / 10000 = 3.23 tiles