Answer:
The sculpture must be 5 inches wide, 5 inches tall, and 10 inches long.
Step-by-step explanation:
Let the dimensions of the sculpture be l, w and h.
[tex]\rm V = lwh[/tex]
Given:
- [tex]\rm h= w = l - 5[/tex]
Substitute the given value of the variables.
[tex]\implies \rm 250 = (l)(l-5)(l-5)[/tex]
[tex]\implies \rm 250 = (l^2-5l)(l-5)[/tex]
[tex]\implies \rm 250 = l^3-10l^2+25l[/tex]
[tex]\implies \rm l^3-10l^2 + 25l - 250 = 0[/tex]
[tex]\implies \rm (l - 10)(l^2+25) = 0[/tex]
[tex]\rm If \ l -10 = 0, then \ l= 10[/tex]
[tex]\rm If \ l^2+25 = 0,then \ l = 5i, which \ is\ unrealistic[/tex]
∴ l = 10.
Now, lets solve for the other dimensions.
[tex]\rm h = w = l - 5[/tex]
Substitute the value of l.
[tex]\implies \rm h = w = 10 - 5[/tex]
[tex]\implies \rm h = w = 5[/tex]
Therefore the sculpture must be 5 inches wide, 5 inches tall and 10 inches long.
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