Question

△efg≅△rst. find st.
e 2x g
2x - 1
f r
3x - 2 t
(not drawn to scale)
a 2
b 6
c 3
d 4

Explanation:

Step1: Use property of congruent triangles

Since $\triangle EFG\cong\triangle RST$, corresponding sides are equal. Side $FG$ corresponds to side $ST$. So $2x - 1=3x - 2$.

Step2: Solve for x

Subtract $2x$ from both sides: $- 1=x - 2$. Then add 2 to both sides: $x = 1$.

Step3: Find length of ST

Substitute $x = 1$ into the expression for $ST$ which is $3x - 2$. So $ST=3\times1 - 2=1$. But there seems to be an error above, if we assume $EG$ corresponds to $ST$ (since no clear - cut corresponding - side indication in the problem setup, and if we go by the most likely match based on naming order), then $2x=3x - 2$.

Step4: Solve new equation for x

Subtract $2x$ from both sides: $0=x - 2$. Add 2 to both sides: $x = 2$.

Step5: Find length of ST

Substitute $x = 2$ into the expression for $ST$ (which is $3x - 2$). So $ST=3\times2 - 2=4$.

Answer:

D. 4