A man paved his square courtyard with square tiles. After this, he wanted to increase the courtyard and bought 324 more tiles of the same size. These were added onto the existing courtyard to make a bigger one in square shape. Find the total number of tiles used to make the bigger courtyard. [4 MARKS]

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Solution

Concept: 1 Mark
Application: 2 Marks
Answer: 1 Mark

At first, the number of tiles used by man $= x^{2}$

Let the number of tiles after adding 324 more tiles to the original number of tiles be $y^{2}$

$x^{2} + 324 = y^{2}$

On observing the above equation, it is known that the pythagorean triplet 18, 24, 30 satisfy the above equation.

So, x = 24 and y = 30

So, the number of tiles he used altogether $= 30^{2} = 900$

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