Question

The volume of this triangular prism is 247.5 cubic inches. What is the value of t?

Answer 1

Volume of a triangle is 1/2 base x height x length.

Using the given information we can find t:

247.5 = 1/2(5)(t)(11)

Simplify:

247.5 = 2.5(t)(11)

247.5 = 27.5t

Divide both sides by 27.5:

t = 247.5 / 27.5

t = 9

Answer 2

Answer:

t = 9in

Step-by-step explanation:

The formula of a volume of a prism:

$V=BH$

B - area of a base

H - height

In the base is the triangle.

The formula of an area of a triangle:

$A=\dfrac{bh}{2}$

b - base

h - height

We have V = 247.5 in³, b = 5 in, H = 11 in and h = t.

Therefore:

$B=\dfrac{5t}{2}$

Put them to the formula of a volume:

$247.5=\left(\dfrac{5t}{2}\right)(11)$

$247.5=\dfrac{55t}{2}$

$247.5=27.5t$              divide both sides by 27.5

$9=t\to t=9\ in$