If the length of a square is increased by 20% while while its width is decreased by 20% to form a rectangle, what is the ratio of the area of the rectangle to the area of the square?
Let the length of the square be \( L \). The area of the square is:
\(A_s = L^2\)
After modifications, the new length \( L_r \) and width \( W_r \) of the rectangle are:
\(L_r = 1.2L, \quad W_r = 0.8L\)
The area of the rectangle \( A_r \) is:
\(A_r = L_r \times W_r = (1.2L)(0.8L) = 0.96L^2\)
The ratio of the areas is:
\(\text{Ratio} = \frac{A_r}{A_s} = \frac{0.96L^2}{L^2} = 0.96\)
Thus, the ratio of the area of the rectangle to the area of the square is \( 0.96 \). Or \(\frac{96}{100}\) = 24:25
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