Ineed ! the ratio of the length to the width to the height of a rectangular box of cereal is 6: 2: 7. the sum of the length and the width of the box is 24 centimeters. find the surface area of the box of cereal

Given the ratio, you know that:
length = 6x
width = 2x
height = 7x

Because the sum of the length and the width is 24 cm, you can write the equation:
6x + 2x = 24
Solve:
8x = 24
x = 3

Plug the 3 back into the expressions written earlier for length, width, and height.
length = 18 cm
width = 6 cm
height = 21 cm

Use the formula SA = 2B + Ph to solve for the surface area.
Surface Area = 2(area of the base) + (perimeter of the base)(height)

I'm going to plug in l, w, and h as variables for length, width, and height to show the exact way to solve for the B and P.
SA = 2lw + 2(l + w)h
SA = 2(18)(6) + 2(18 + 6)(21)
SA = 216 + 2(24)(21)
SA = 216 + 1008
SA = 1224

The surface area is 1,224 cm^2.