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

Answer:

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

Step-by-step 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 $10x^2+38x+30$.