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 $30$ $30$ $f t^{2}$ $ft^2$ . The length is 1 less than 3 times the width. How wide should the metal piece be?

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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 $30$ $30$ $f t^{2}$ $ft^2$ . The length is 1 less than 3 times the width. How wide should the metal piece be?

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Answer 1 · 2016-02-17T00:04:05

Draw a diagram to represent the situation.

Explanation:

![https://en.wikipedia.org/wiki/Rectangle]( useruploads.socratic.org )

The formula for area of a rectangle is $A = L \times W$ $A = L xx W$ .

We know:

L = 3x - 1

W = x

A= 30

All we have to do is solve for x.

$A = L \times W$ $A = L xx W$

$30 = (3 x - 1) \times x$ $30 = (3x - 1) xx x$

$30 = 3 x^{2} - x$ $30 = 3x^2 - x$

$0 = 3 x^{2} - x - 30$ $0 = 3x^2 - x - 30$

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

$0 = 3 x^{2} + 9 x - 10 x - 30$ $0 = 3x^2 + 9x - 10x - 30$

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

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

$x = \frac{10}{3} and - 3$ $x = 10/3 and -3$

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

The dimensions of the piece of metal would be $\frac{10}{3} \times 9$ $10/3 xx 9$ feet.

Practice exercises:

A rectangle has an area of $72 c m^{2}$ $72 cm^2$ . The length measures two more than four times the width. Find the perimeter of the rectangle.
A right triangle has two legs and a hypotenuse. The hypotenuse measures $\sqrt{1000}$ $sqrt(1000)$ inches. The longer leg measures ten less than the double of the shorter leg. Find the area of the triangle.
A rectangle has a perimeter of 46 meters. Its area is $126 m e t e r s^{2}$ $126 meters^2$ .

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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 $30$ $30$ $f t^{2}$ $ft^2$ . The length is 1 less than 3 times the width. How wide should the metal piece be?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

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 3030 ft2ft^2. The length is 1 less than 3 times the width. How wide should the metal piece be?

1 Answer

Explanation:

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Impact of this 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 $30$ $30$ $f t^{2}$ $ft^2$ . The length is 1 less than 3 times the width. How wide should the metal piece be?