Question

a farmer wants to plant three rectangular fields so that the widths are the same. the areas of the fields, in square yards, are given by the expressions 12x^3y , 6xy^4 , 21xy. what is the greatest possible widths of the fields if x=3 and y=2.

Answer 1

The widths of the three fields are the same and equal to x, since that is the variable used in the expressions for the areas of the fields.

To find the greatest possible width, you need to find the highest value of x that satisfies the given conditions. You can substitute x=3 and y=2 in the expressions for the areas of the fields and compare them.

Area of field 1 = 12x^3y = 12 * 3^3 * 2 = 12 * 27 * 2 = 648 square yards Area of field 2 = 6xy^4 = 6 * 3 * 2^4 = 6 * 3 * 16 = 288 square yards Area of field 3 = 21xy = 21 * 3 * 2 = 126 square yards

All three fields have the same width of x = 3 yards, and the width is the greatest possible width.