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If the smaller dimension of a rectangle is increased by 3 feet and the larger dimension by 5 feet, one dimension becomes $$\frac{3}{5}$$ of the other, and the area is increased by 135 square feet. Find the original dimensions. Solution:
Representations
SymbolsMeaning
$$L$$Length of the rectangle
$$W$$Width of the rectangle
$$L_n$$New length of the rectangle
$$W_n$$New width of the rectangle

$$L_n= L+5$$

$$L = L_n -5$$

$$W_n= W+3$$

$$W = W_n -3$$

$$W_n= \frac{3}{5} L_n$$

$$W = \frac{3}{5} L_n -3$$

$$A_n= A+135$$

$$L_n W_n= LW+135$$

$$L_n ( \frac{3}{5} L_n)= LW+135$$

$$\frac{3}{5} L_n ^2= ( L_n -5)(\frac{3}{5}L_n -3)+135$$

$$\frac{3}{5} L_n ^2= \frac{3}{5}L_n^2-3L_n -3L_n + 15)+135$$

$$L_n = 25$$

$$L = 25-5 = 20$$

$$L = \frac{3}{5}(25)-3 = 12$$

Thus the original dimensions is: 12x20 \text{feet}