A triangular prism has base edges 3 cm, 5 cm, and 7 cm long. Its lateral area is 285 cm? What is the height of the prism?

The height is 24 centimeters

Step-by-step explanation:

The perimeter of the triangle base is P = a+b+c = 4+6+7 = 17 cm long.

The lateral surface area (abbreviated LSA) of any prism can be found using this formula

LSA = P*h

where P is the perimeter along the base and h is the height of the prism.

We're given the lateral area of 408, so LSA = 408.

Let's use that LSA value, along with P = 17 as well to solve for h.

LSA = P*h

408 = 17*h

408/17 = 17*h/17

24 = h

h = 24

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.