Answer:
t = 9in
Step-by-step explanation:
The formula of a volume of a prism:
[tex]V=BH[/tex]
B - area of a base
H - height
In the base is the triangle.
The formula of an area of a triangle:
[tex]A=\dfrac{bh}{2}[/tex]
b - base
h - height
We have V = 247.5 in³, b = 5 in, H = 11 in and h = t.
Therefore:
[tex]B=\dfrac{5t}{2}[/tex]
Put them to the formula of a volume:
[tex]247.5=\left(\dfrac{5t}{2}\right)(11)[/tex]
[tex]247.5=\dfrac{55t}{2}[/tex]
[tex]247.5=27.5t[/tex] divide both sides by 27.5
[tex]9=t\to t=9\ in[/tex]
