Question : If $\Delta \mathrm{XYZ} \cong \Delta \mathrm{LMR}$, then $m+x+p=?$
Option 1: 7
Option 2: 6
Option 3: 9
Option 4: 13
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Correct Answer: 9
Solution :
Given: $\Delta \mathrm{XYZ} \cong \Delta \mathrm{LMR}$
$\Delta \mathrm{XYZ}$ and $\Delta \mathrm{LMR}$ are congruent triangles.
We can say, $\mathrm{XY=LM}$
⇒ $2m+1=5$
⇒ $m=2$
$\mathrm{YZ=MR}$
⇒ $2p+2=8$
⇒ $p=3$
$\mathrm{ZX=RL}$
⇒ $2x–1=7$
⇒ $x=4$
So, $m+x+p=2+3+4$
⇒ $m+x+p=9$
Hence, the correct answer is 9.
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