Question

the volume of a rectangular box is 130 cubic inches. the height of the box is 1 inch. the width of the box is 3 inches less than the length. which equation can you use to find w, the width of the box in inches? $(w + 1)(w + 3) = 130$ $(w + 1)(w - 3) = 130$ $1(w - 3) = 130$ $w(w - 3) = 130$ $1(w + 3) = 130$ $w(w + 3) = 130$ now, use the equation you picked to find w. $w = square$ inches submit

Explanation:

Part 1: Finding the Correct Equation

Step1: Recall Volume Formula

The volume \( V \) of a rectangular box is given by \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height.

Step2: Define Variables

Given \( h = 1 \) inch, \( w \) is width, and width is 3 inches less than length, so \( l = w + 3 \).

Step3: Substitute into Volume Formula

Substitute \( l = w + 3 \), \( w = w \), \( h = 1 \) into \( V = l \times w \times h \): \( 1 \times w \times (w + 3) = 130 \), which simplifies to \( w(w + 3) = 130 \).

Step1: Expand the Equation

\( w(w + 3) = 130 \) becomes \( w^2 + 3w - 130 = 0 \).

Step2: Factor the Quadratic

Factor \( w^2 + 3w - 130 \): find two numbers that multiply to -130 and add to 3. The numbers are 13 and -10. So, \( (w + 13)(w - 10) = 0 \).

Step3: Solve for \( w \)

Set each factor to zero: \( w + 13 = 0 \) (gives \( w = -13 \), invalid as width can't be negative) or \( w - 10 = 0 \) (gives \( w = 10 \)).

Answer:

\( w(w + 3) = 130 \)

Part 2: Solving for \( w \)