Respuesta :
Answer:
16 m.
Step-by-step explanation:
First, we can start by expressing the length and height each as an equation using the variables h, w, and l. Also, we can write the formula for volume, as V.
h = 5w
l = 8h
V = l × w × h
Now, we can use the equations for length and width to substitute into each other and the equation for volume to restrict the equation to only 2 variables (V and w).
h = 5w --> l = 8h --> l = 8(5w)
V = 8(5w) × w × 5w = 200w³
Because we were given a value for volume, we can plug it into the equation.
(12.8 m³) = 200w³
Now, we can solve for w.
(12.8 m³) / 200 = (200w³) / 200
(0.064 m³) = w³
[tex]\sqrt[3]{(0.064m^{3} )}[/tex] = [tex]\sqrt[3]{w^{3} }[/tex]
(0.4 m) = w
Finally, now that we have the width, we can plug w into our original equation for length (l).
l = 8(5w)
l = 8(5(0.4 m)) = 16 m
So, our answer is the wall's length is 16 m!
