Triangles ABC and A'B'C are similar. This means that the corresponding sides are in the same ratio, in this case:
Replacing with data:
Answer:
length = 76 cm
Step-by-step explanation:
The perimeter = (2 × width) + (2 × length)
264 = (2×56) + (2 × length)
264 = 112 + (2 × length)
264 - 112 = 2 × length
152 = 2 × length
152/2 = length
76 = length
length = 76 cm
Let
b-----------> the length side of the square box
h------------> the height of the box
SA---------> surface area of the box
we know that
[volume of the box]=b²*h
volume=256 in³
b²*h=256-------> h=256/b²-----> equation 1
surface area of the box=area of the base+perimeter of base*height
area of the base=b²
perimeter of the base=4*b
surface area=b²+(4*b)*h------> SA=b²+4*b*h-----> equation 2
substitute equation 1 in equation 2
SA=b²+4*b*[256/b²]-----> SA=b²+1024/b-----> SA=(b³+1024)/b
the answer is
the formula of the volume of the box is V=b²*h-----> 256=b²*h
the formula of the surface area of the box are
SA=b²+4*b*h
SA=(b³+1024)/b
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