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20 PTS!!!!!!!!!!!!!!!!!!!!! PLEASEEEE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Triangular prisms M and N are congruent. If one triangular face of prism M has area 8 in2, and the surface area of prism N is 166 in2, what is the area of one rectangular face from prism M?
A) 40 in2
B) 45 in2
C) 50 in2
D) 55 in2

20 PTS PLEASEEEE HELP Triangular prisms M and N are congruent If one triangular face of prism M has area 8 in2 and the surface area of prism N is 166 in2 what i class=

Respuesta :

calculista

Answer:

Option C. [tex]50\ in^{2}[/tex]

Step-by-step explanation:

In this problem I assume that the triangular base is an equilateral triangle

we know that

Triangular prisms M and N are congruent

so

If the surface area of prism N is 166 in2

then

the surface area of prism M is 166 in2 too

The surface area of the prism is equal to

[tex]SA=2B+3C[/tex]

where

B is the area of one triangular face

C is the area of one rectangular face

In this problem we have

[tex]SA=166\ in^{2}[/tex]

[tex]B=8\ in^{2}[/tex]

substitute and solve for C

[tex]166=2(8)+3C[/tex]

[tex]3C=166-16[/tex]

[tex]3C=150[/tex]

[tex]C=50\ in^{2}[/tex]

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