Find the Mass and the Center of Mass of the Lamina

Multiple Choice

Find the mass and the center of mass of the lamina occupying the region R, where R is the triangular region with vertices $( 0,0 ) \text {, }$ $( 2,5 )$ and $( 4,0 )$ , and having the mass density $\rho ( x , y ) = x$

A) $m =$ $25$ , $( \bar { x } , \bar { y } ) = \left( \frac { 7 } { 3 } , \frac { 5 } { 3 } \right)$
B) $m = 20$ , $( \bar { x } , \bar { y } ) = \left( \frac { 7 } { 3 } , \frac { 5 } { 3 } \right)$
C) $m =$ $25$ , $( \bar { x } , \bar { y } ) = \left( \frac { 5 } { 3 } , \frac { 7 } { 3 } \right)$
D) $$m = 20$$ , $( \bar { x } , \bar { y } ) = \left( \frac { 5 } { 3 } , \frac { 7 } { 3 } \right)$