Question

Lorene Play is to make several open top boxes in which to carry plans please check photo

Answer 1

Given:

Find-:

Dimensions of the cardboard

Explanation-:

The volume of a quadrangular prism is:

`V=l* w* h`

The length is 12 more than the width is:

`\begin{gathered} \text{ Width =}y \\ \\ \text{ Length =}y+12 \end{gathered}`

Hight is 6.

So the Area is:

`\begin{gathered} V=l* w* h \\ \\ V=(y+12)*(y)*(6) \\ \\ V=6y(y+12) \\ \end{gathered}`

Given that volume is 2958 so,

`\begin{gathered} 6y(y+12)=2958 \\ \\ y(y+12)=(2958)/(6) \\ \\ y^2+12y=493 \\ \\ y^2+12y-493=0 \end{gathered}`

Solve the quadratic equation is:

`\begin{gathered} ax^2+bx+c=0 \\ \\ x=(-b\pm√(b^2-4ac))/(2a) \end{gathered}`

`\begin{gathered} y^2+12y-493=0 \\ \\ y=(-12\pm√(12^2-4(1)(-493)))/(2) \\ \\ y=(-12\pm√(2116))/(2) \\ \\ y=(-12\pm46)/(2) \\ \\ y=-6\pm23 \\ \\ y=-6-23;y=-6+23 \\ \\ y=-29,y=17 \end{gathered}`

A negative value is not considered because sides are always positive so y is 17.

So the width is 17 and length is:

`\begin{gathered} \text{ Length}=y+12 \\ \\ \text{ Length =}17+12 \\ \\ \text{ Length =}29 \end{gathered}`

So dimensions are 29 in. by 17 in.