Question

Matilda covers the interior faces of a kitchen drawer with shelf paper. The height of the drawer is 3/4 its width and the depth front to back is 7/4 its width. if the exact amount of shelf paper needed is 846 square inches what is the depth of the drawer? help me I need help

Answer 1

To know the depth of the drawer you need to know that the shelf paper is the area of the interior faces of the drawer, then:

A = 846sq in

the area is equal to:

`A=A_b+A_l`

Where:

Ab is the area of the base of the drawer

Al is the area of the laterals of the drawer

The Area of the base is:

`A_b=(7)/(4)x\cdot x=(7)/(4)x^2`

And the area of the laterals is the sum of the area of every lateral:

`A_l=2\lbrack((3)/(4)x)\cdot((7)/(4)x)\rbrack+2\lbrack((3)/(4)x)\cdot(x)\rbrack`
`A_l=(21)/(8)x^2+(3)/(2)x^2=(33)/(8)x^2`

Then:

`846=(7)/(4)x^2+(33)/(8)x^2`
`846=(188)/(32)x^2=(47)/(8)x^2=5.87x^2`

The we clear the x:

`(846)/(5.87)=x^2`
`\sqrt[]{144.12}=x`
`x=12.004in`The depth of the drawer is x= 12,004 inches