A box is to be constructed with a rectangular base and a height of 5 cm.If the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box? V=Iwh P=2(I+w) y=5(28-x)(x) y=5(28-2x)(x) y=5(14-x)(x) y=5(14-2x)(x)

## Step 1<br />The problem involves the construction of a box with a rectangular base and a height of 5 cm. The perimeter of the base is given as 28 cm. We are asked to find the quadratic equation that best models the volume of the box.<br /><br />## Step 2<br />The perimeter of a rectangle is given by the formula \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width of the rectangle. Given that the perimeter is 28 cm, we can set up the equation \(28 = 2(l + w)\).<br /><br />## Step 3<br />We can solve this equation for \(l\) to get \(l = 14 - w\).<br /><br />## Step 4<br />The volume of a rectangular box is given by the formula \(V = lwh\), where \(h\) is the height of the box. In this case, the height is given as 5 cm, so we can substitute \(h = 5\) into the volume formula to get \(V = lw \cdot 5\).<br /><br />## Step 5<br />Substituting \(l = 14 - w\) into the volume formula, we get \(V = (14 - w)w \cdot 5\), which simplifies to \(V = 5(14 - w)w\).<br /><br />## Step 6<br />This equation is a quadratic equation in the form \(y = ax^2 + bx + c\), where \(a = 5\), \(b = -14\), and \(c = 0\). Therefore, the correct answer is \(y = 5(14 - w)w\).