Question

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?

Answer 1

Draw a diagram to represent the situation.

Explanation:

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!