One more rectangular-shaped piece of metal siding needs to be cut to cover the exterior of a pole barn. The area of the piece is #30# #ft^2#. The length is 1 less than 3 times the width. How wide should the metal piece be?

The formula for area of a rectangle is #A = L xx W#.

We know:

L = 3x - 1

W = x

A= 30

All we have to do is solve for x.

#A = L xx W#

#30 = (3x - 1) xx x#

#30 = 3x^2 - x#

#0 = 3x^2 - x - 30#

This trinomial is factorable. Since it is of the form #y = ax^2 + bx + c#, you must find two numbers that multiply to #ac# and that add to b. Two numbers that multiply to -90 and that add to -1 are -10 and 9.

#0 = 3x^2 + 9x - 10x - 30#

#0 = 3x(x + 3) - 10(x + 3)#

#0 = (3x - 10)(x + 3)#

#x = 10/3 and -3#

Since a negative side length is impossible, the width must measure #10/4#. As a result, the width measures #3(10/3) - 1 = 9#.

The dimensions of the piece of metal would be #10/3 xx 9# feet.

Practice exercises:

1. A rectangle has an area of #72 cm^2#. The length measures two more than four times the width. Find the perimeter of the rectangle.

2. A right triangle has two legs and a hypotenuse. The hypotenuse measures #sqrt(1000)# inches. The longer leg measures ten less than the double of the shorter leg. Find the area of the triangle.

3. A rectangle has a perimeter of 46 meters. Its area is #126 meters^2#.

Good luck!