Question

a mailing container for posters is made from 87.4 square inches of cardboard the container is in the shape of a triangular prism the base of the prism is an equilateral triangle with 2- inch side lengths and a height of 1.7 inches what is the length of the container

Answer 1

The length of the container is
`14\ in`

Explanation:

we know that

The surface area of a triangular prism (a mailing container) is equal to

`SA=2B+PL`

where

B is the area of the triangular base

P is the perimeter of the triangular base

L is the length of the container

step 1

Find the area of the base B

`B=(1)/(2)(2)(1.7)=1.7\ in^(2)`

step 2

Find the perimeter of the base P

`P=3(2)=6\ in`

step 3

Find the length L of the container

we have

`SA=87.4\ in^(2)`

`B=1.7\ in^(2)`

`P=6\ in`

substitute and solve for L

`87.4=2(1.7)+(6)L`

`L=[87.4-2(1.7)]/(6)`

`L=14\ in`