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 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

Answer 1

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.

Answer 2

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.