A triangular prism has bade edges 5cm, 6cm, and 8cm long. It’s lateral area is 323cm squared. What is the height of the prism?

17 cm

Step-by-step explanation:

The lateral surface area of a prism is the sum of the surface areas of the sides of the prism.

Since the bases of the prism are triangles, there are three sides.  The area of each lateral is the product of a side of the triangle times the height of the prism.  

We can express this as Lateral Surface Area  LSA = (s1xh) + (s2xh) + (s3+h), where "s1, s2, s3" are the lengths of the sides of the triangle and "h" is the height of the prism.

We can factor out "h" to get   LSA = hx(s1+s2+s3)  where the factor "s1+s2+s3" is the perimeter of the triangle.

Solving for "h", we get   h = LSA / (s1+s2+s3)

For your specific problem,   h =  323 / (5 + 6 +8 )   =  17 cm

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6

it is c, trust i got your back lol

step-by-step explanation: