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Question

# One square has sides 6 cm long. Another has sides 9 cm long. Find the ratio of the areas of the squares.

Solution

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$\\ \dfrac{A_{2}}{A_{1}} = \dfrac{6^{2}}{9^{2}}$

$\\ \dfrac{A_{2}}{A_{1}} = \dfrac{36}{81}$

$\\ \dfrac{A_{2}}{A_{1}} = \dfrac{36 \div 9}{81 \div 9}$

$\\ \dfrac{A_{2}}{A_{1}} = \dfrac{4}{9}$

The ratios of the areas is the same as the ratio of the second powers of the sides. $\\A_{1}$.......area of the bigger square $\\A_{2}$.......area of the smaller square

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