tmua None Q12

tmua · Uk · specimen_paper1 Applied differentiation Applied modeling with differentiation
12. The cross-section of a triangular prism is an equilateral triangle with side $2 x \mathrm {~cm}$. The length of the prism is $d \mathrm {~cm}$.
Let the total surface area of the prism be $T \mathrm {~cm} ^ { 2 }$. Given that the volume of the prism is $T \mathrm { cm } ^ { 3 }$, which one of the following is an expression for $d$ in terms of $x$ ?
A $\frac { x } { 2 x - 3 }$
B $\frac { 3 x } { 3 x - 2 \sqrt { 3 } }$
C $\frac { 2 x } { x - 4 \sqrt { 3 } }$
D $\frac { 2 x } { x - 2 \sqrt { 3 } }$
E $\frac { 2 x } { x - \sqrt { 3 } }$
12. The cross-section of a triangular prism is an equilateral triangle with side $2 x \mathrm {~cm}$. The length of the prism is $d \mathrm {~cm}$.

Let the total surface area of the prism be $T \mathrm {~cm} ^ { 2 }$. Given that the volume of the prism is $T \mathrm { cm } ^ { 3 }$, which one of the following is an expression for $d$ in terms of $x$ ?

A $\frac { x } { 2 x - 3 }$

B $\frac { 3 x } { 3 x - 2 \sqrt { 3 } }$

C $\frac { 2 x } { x - 4 \sqrt { 3 } }$

D $\frac { 2 x } { x - 2 \sqrt { 3 } }$

E $\frac { 2 x } { x - \sqrt { 3 } }$\\