Find the equations

Question

a farmer has a rectangular pigpen that the length is 4 feet more than 3 times its width, and the pin has an area of 175 square feet. what are 2 equations that would be used in the calculator to determine the length and width? Quadratic function needed

Answer 1

W = 7 feet

L = 25 feet

The quadratic can be obtained from the information given as follows

A = L * W

L = 3W + 4 (this can be used in a calculator to determine the Length, L)

So

175 = W(3W + 4)

175 = 3W² + 4W

Subtract 175 from both sides of the equation

0 = 3W² + 4W - 175

Your quadratic is also above and it can be factored to find W

0 = (3W + 25)(W - 7)

W cannot be negative so W = 7

Substitute this value in L = 3W + 4

L = 3(7) + 4 = 21 + 4 = 25

The rectangle is 25 x 7

You can check this in the formula for the area

A = L * W

175 = 25 * 7

175 = 175

You have a couple choices as to what to use in the calculator, you can use the formula for the area of a rectangle once the width is determined to solve for the length. You can use the relationship between the length and width given in the problem.

I hope you find this useful.