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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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A2A1=6292\\ \dfrac{A_{2}}{A_{1}} = \dfrac{6^{2}}{9^{2}}

A2A1=3681\\ \dfrac{A_{2}}{A_{1}} = \dfrac{36}{81}

A2A1=36÷981÷9\\ \dfrac{A_{2}}{A_{1}} = \dfrac{36 \div 9}{81 \div 9}

A2A1=49\\ \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. A1\\A_{1}.......area of the bigger square A2\\A_{2}.......area of the smaller square

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