128
The dimensions of a window are $156$ cm $\times 216$ cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.
Show SolutionHide Solution↓
Sol. $156 = 2 \times 2 \times 3 \times 13 = 2^2 \times 3 \times 13$ (I Mark)
$216 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 = 2^3 \times 3^3$ (II Mark)
$\therefore$ Required side length of the square = HCF($156,216$) = $12$ cm (III Mark)
Number of squares formed = $\frac{156 \times 216}{12 \times 12} = 234$ (IV Mark)
$216 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 = 2^3 \times 3^3$ (II Mark)
$\therefore$ Required side length of the square = HCF($156,216$) = $12$ cm (III Mark)
Number of squares formed = $\frac{156 \times 216}{12 \times 12} = 234$ (IV Mark)