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Question

A square carpet of side length 9 feet is designed with one large shaded square and eight smaller, congruent shaded squares, as shown. FIGURE If the ratios 9:S and S:T are both equal to 3 and S and T are the side lengths of the shaded squares, what is the total shaded area?

Accepted Answer

We are given that 9S=ST=3. 9S=3 gives us S=3, so ST=3 gives us T=1. There are 8 shaded squares with side length T and there is 1 shaded square with side length S, so the total shaded area is 8(11)+1(33)=8+9=17.