Answer:
The bases are congruent.
The volume of the first solid is twice as much as the volume of the second solid.
If the dimensions of the second solid are x by x by h, the first solid has 4xh more surface area than the second solid.
Step-by-step explanation:
From the above answers; the term congruent means two similar objects or shapes having the same pattern or structure. From the question; we are being told that the two rectangular solid have a square base hence; they are both congruent in nature .
Also;
The volume of the first solid is twice as much as the second solid . i.e 2:1
If the volume of the first solid is : [tex]x*x*2 \ h[/tex] = [tex]2x^2 \ h[/tex]
Then the volume of the second solid is = [tex]x*x*h = x^2h[/tex]
thus ; they are in the ratio of 2:1
FInally: If the dimensions of the second solid are x by x by h, the first solid has 4xh more surface area than the second
The surface area of the first solid is :
[tex]=2[x*x+(2 H*x+2 H*x)] \\ \\ =2[x^2+4 Hx] \\ \\ = 2x[x + 4Hx][/tex]
Then the second solid is :
[tex]2[x*x+x* H+ H*x] \\ \\ =2[x^2+2 Hx] \\ \\ =2x[x+ 2H][/tex]
Therefore:
[tex]S_1 = S_2 + 4Hx[/tex]
