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 1The 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.## Step 2The perimeter of a rectangle is given by the formula \(P = 2(l + w)\), where is the length and is the width of the rectangle. Given that the perimeter is 28 cm, we can set up the equation \(28 = 2(l + w)\).## Step 3We can solve this equation for to get .## Step 4The volume of a rectangular box is given by the formula , where is the height of the box. In this case, the height is given as 5 cm, so we can substitute into the volume formula to get .## Step 5Substituting into the volume formula, we get \(V = (14 - w)w \cdot 5\), which simplifies to \(V = 5(14 - w)w\).## Step 6This equation is a quadratic equation in the form , where , , and . Therefore, the correct answer is \(y = 5(14 - w)w\).