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

Answer:

The length of the container is $14\ in$

Step-by-step 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

$B=\frac{1}{2}(2)(1.7)=1.7\ in^{2}$

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

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

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

$L=14\ in$