A farmer has 1050 yd of fencing to enclose a rectangular pasture for her goats. Since one side of the pasture borders a river, that side does not need to be fenced. The sides of length a must be three times as long as side b. Find the dimensions of the rectangular pasture.

Dimensions:

a = 630 yd

b = 210 yd

A = 132.300 yd²

Step-by-step explanation:

Dimensions of rectangular pasture

a and b and a = 3*b a is opposite side at the river, therefore

Area of rectangular pasture

A = a * b and perimeter of rectangular area (with fencing material) is

P = a + 2b or P = 3*b + 2*b ⇒ 1050 = 5*b

b = 1050 / 5 ⇒ b = 210 yd

And as a = 3*b ⇒ a = 3*210 ⇒ a = 630 yd

And the area is A = 630*210 = 132.300 yd²