Find the surface area of the prism.

answer:

x = 96.23   if   x is the area of the base

x =21           if x is the side length of the base

step-by-step explanation:

the volume of a square pyramid is given by

v=1/3 a^ 2 h

we know the volume is 441 and the area of the base is a^2 which is x

and the height is 1/7x

substituting these values in

441 = 1/3 (x) 1/7x

441 =1/21 x^2

multiply each side by 21

441*21 = 21*1/21 x^2

9261 = x^2

take the square root of each side

sqrt(9261) = sqrt(x^2)

x = 96.23

i am thinking you mean x is the side length on the base

we know the volume is 441 and the area of the base is a^2 which is x^2

and the height is 1/7x

substituting these values in

441 = 1/3 (x^2) 1/7x

441 =1/21 x^3

multiply each side by 21

441*21 = 21*1/21 x^3

9261 = x^3

take the cube root of each side

(9261) ^ (1/3) = (x^3)^(1/3)

21 =x

answer:

the numbers are 6 and 4

step-by-step explanation:

let x = integer

the second is x-2

product of x*(x-2)   is 24

x(x-2) = 24

distribute

x^2 -2x =24

subtract 24 from each side

x^2 -2x -24 =24-24

x^2 -2x-24 =0

factor

what two number multiply together to give 24 and add to -2

-6*4= -24

-6+4 = -2

(x-6) (x+4) =0

using the zero product property

x-6 =0     x+4 = 0

x=6       x=-4

the question states the number is positive

x=6

the second number is x-2 = 4

the numbers are 6 and 4