Question

you are painting the outside of a jewery box, including the bottom. To find the surface area(S.A) of the jewlery box, you can use the formula S.A+2wl+2lh+2wh, where l os the length, w is the width, and h is the height. What is the surface earea of the jewlery box in terms of x?

Answer 1

`SA=10x^2+38x+30`

Explanation:

Please consider the complete question.

You are painting the outside of a jewelry box including the bottom. To find the surface area (S.A) of the jewelry box, you can use the formula
`SA=2wl+2lh+2wh`, where L is length, W is width, and H is height. What is the surface area of the jewelry box in terms of x."

`L = 2x+5`

`W= x`

`H= x+3`

To find the surface area of box in terms of x, we will substitute the given values of length, width, and height in terms of x as:

`SA=2x(2x+5)+2(2x+5)(x+3)+2x(x+3)`

Now, we will use distributive property
`a(b+c)=ac+ac` to simplify our expression as:

`SA=4x^2+10x+(4x+10)(x+3)+2x^2+6x`

`SA=4x^2+10x+4x(x+3)+10(x+3)+2x^2+6x`

`SA=4x^2+10x+4x^2+12x+10x+30+2x^2+6x`

Let us combine like terms.

`SA=4x^2+4x^2+2x^2+10x+12x+10x+6x+30`

`SA=10x^2+38x+30`

Therefore, the surface area of the jewelry box in terms of x would be
`10x^2+38x+30`.