To find the dimensions of the second rectangular prism that will have the same surface area as the first one, we can use the formula for the surface area of a rectangular prism which is:
Surface Area = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height of the rectangular prism.
For the first rectangular prism, we have:
l = 3 m w = 7 m h = 4 m
Surface Area = 2lw + 2lh + 2wh Surface Area = 2(3)(7) + 2(3)(4) + 2(7)(4) Surface Area = 42 + 24 + 56 Surface Area = 122 m²
To find the dimensions of the second rectangular prism that will have the same surface area as the first one, we can use this formula again and solve for one of the variables. Let’s solve for l:
Surface Area = 2lw + 2lh + 2wh 122 = 2l(w+h) + 2wh 122 = 2l(w+h) + w(4) 122 = 2l(w+h) + 4w 118 = l(w+h)
Now we can choose any value for w and h and solve for l. Let’s choose w=1 and h=1:
118 = l(1+1) 118 = l(2) l = 59
So the dimensions of the second rectangular prism that will have the same surface area as the first one are:
l = 59 m w = 1 m h = 1 m