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The emphasis is on conceptual understanding, analytical thinking and problem solving rather than simply memorising formulas and standard methods.

The objective is to help students understand what they are learning and develop the ability to solve problems they have not seen before.

A 5.25 m by 3.78 m rectangular courtyard ...

A 5.25 m by 3.78 m rectangular courtyard is to be paved with square tiles of the same size such that only whole tiles are used. What is the largest possible size of such a tile? Also, find the number of tiles required.

Solution


Let a be the edge of the square tile.

Then, $a\times m=5.25$ and $a\times n=3.78$

Dividing, $\frac {m}{n}=\frac {525}{378}$

= $\frac {175}{126}$ [dividing by 3]

= $\frac {25}{18}$ [dividing by 7]

Smallest value of m = 25 and smallest value of n = 18 (for the square tile to be of largest size, m & n should be the least)

Number of tiles = m.n = 25 x 18 = 450

PS: The solution in file format is embedded below.