Question

# A rectangular sheet of paper is $12\frac{1}{2}cm$ long and $10\frac{2}{3}cm$ wide. Find the perimeter.

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Solution

## Length of the rectangle $=12\frac{1}{2}cm$Here we have a mixed fraction convert into an improper fraction. $=\frac{2×12+1}{2}\phantom{\rule{0ex}{0ex}}=\frac{24+1}{2}\phantom{\rule{0ex}{0ex}}=\frac{25}{2}$The breadth of the rectangle $=10\frac{2}{3}cm$ $=\frac{3×10+2}{3}\phantom{\rule{0ex}{0ex}}=\frac{30+2}{3}\phantom{\rule{0ex}{0ex}}=\frac{32}{3}$The perimeter of a rectangle $=2$ (length $+$ breadth) $=2×\left(\frac{25}{2}+\frac{32}{3}\right)\phantom{\rule{0ex}{0ex}}=2×\left(\frac{25×3}{2×3}+\frac{32×2}{3×2}\right)\phantom{\rule{0ex}{0ex}}=2×\left(\frac{75}{6}+\frac{64}{6}\right)\phantom{\rule{0ex}{0ex}}=2×\left(\frac{75+64}{6}\right)\phantom{\rule{0ex}{0ex}}=2×\frac{139}{6}\phantom{\rule{0ex}{0ex}}=\frac{139}{3}$Here we have an improper fraction convert into an improper fraction.Therefore, the perimeter of a rectangle$=46\frac{1}{3}$

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