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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 ft². The length is 1 less than 3 times the width. How wide should the metal piece be? Round to the nearest hundredth of a foot.


A.) 3.33 ft

B.) 4.3 ft

C.) 1 ft

D.) 30 ft

Verified Answer :

meerkat18

Let w be the width of the rectangle. With this representation, length becomes 3w - 1. The area of the rectangular figure is,
                                  A = L x W
where L and W are length and width, respectively. Substituting the known values,
                              30 ft² = (3w - 1)(w)
The value of w from the equation is 3.33 ft.

Answer:

Option A is correct

3.33 ft wide should the metal piece be.

Step-by-step explanation:

Area of rectangle(A) is given by:

\(A =lw\)              .....[1]

l is the length and w is the width of the rectangle respectively.

As per the statement:

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 ft²

⇒A = 30 ft²

It is also given that the length is 1 less than 3 times the width

⇒\(l = 3w -1\) ft

Substitute the given values in [1] we have;

\(30 = (3w-1) \cdot w\)

Using distributive property: \(a \cdot (b+c) = a\cdot b+ a\cdot c\)

then;

\(30 = 3w^2-w\)

We can write this as:

\(3w^2-w-30 = 0\)

Factorize this equation:

Split the middle term we have;

\(3w^2-10w+9w-30 = 0\)

⇒\(w(3w-10)+3(3w-10=0)\)

⇒\((3w-10)(w+3)=0\)

By zero product property we have;

\(3w-10 = 0\) and w+3 = 0

Since, w cannot be negative;

so,

\(w = \frac{10}{3} = 3.3333..\) ft

Therefore, to the nearest hundredth of a foot, 3.33 ft wide should the metal piece be.

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