Surface measurements

Question

During the summer, a rectangular indoor ice skating rink must be covered with square planks for insulation. The rink is 150 feet wide by 270 feet long. The square planks must be purchased in one foot increments and can have a side length no longer than 25 feet. What is the fewest number of square planks that can be used to completely cover the rink’s surface without any gaps or overhang?

Answer 1

The number of square tiles cannot vary for the floor. Find the HCF (highest common factor) of 150 and 270.

150: 2 x 3 x 5 x 5

270: 2 x 3 x 3 x 3 x 5

15 feet squares will work for both lengths. You then find the number of 15 foot lengths in each side:

10 for 150 and 18 for 270 = 10 x 18 = 180 15 feet squares to cover the entire ice skating rink without any overlap or overhang.

Answer 2

Draw a diagram and label!

 

36 tiles of 25 x 25 fill the 150 x 150.

A 60 x 150 strip remains

Fill it with 50 tiles 15 x 15