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

Accepted Solution

Answer:The length of the container is [tex]14\ in[/tex]Step-by-step explanation:we know thatThe surface area of a triangular prism (a mailing container) is equal to[tex]SA=2B+PL[/tex]whereB is the area of the triangular baseP is the perimeter of the triangular baseL is the length of the containerstep 1Find the area of the base B[tex]B=\frac{1}{2}(2)(1.7)=1.7\ in^{2}[/tex]step 2Find the perimeter of the base P[tex]P=3(2)=6\ in[/tex]step 3Find the length L of the containerwe have[tex]SA=87.4\ in^{2}[/tex][tex]B=1.7\ in^{2}[/tex][tex]P=6\ in[/tex]substitute and solve for L[tex]87.4=2(1.7)+(6)L[/tex][tex]L=[87.4-2(1.7)]/(6)[/tex][tex]L=14\ in[/tex]