R (3,0), S (-1,3), and T (0, -2)
R S = ( x 1 − x 2 ) 2 + ( y 1 − y 2 ) 2 = ( 3 − ( − 1 ) ) 2 + ( 0 − 3 ) 2 = 25 = 5 RS=\sqrt{\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}}=\sqrt{\left(3-\left(-1\right)\right)^{2}+\left(0-3\right)^{2}}=\sqrt{25}=5 RS = ( x 1 − x 2 ) 2 + ( y 1 − y 2 ) 2 = ( 3 − ( − 1 ) ) 2 + ( 0 − 3 ) 2 = 25 = 5
R T = ( x 1 − x 2 ) 2 + ( y 1 − y 2 ) 2 = ( 3 − 0 ) 2 + ( 0 − 2 ) 2 = 13 = 3.6 RT=\sqrt{\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}}=\sqrt{\left(3-0\right)^{2}+\left(0-2\right)^{2}}=\sqrt{13}=3.6 RT = ( x 1 − x 2 ) 2 + ( y 1 − y 2 ) 2 = ( 3 − 0 ) 2 + ( 0 − 2 ) 2 = 13 = 3.6
S T = ( x 1 − x 2 ) 2 + ( y 1 − y 2 ) 2 = ( ( − 1 ) − 0 ) 2 + ( 3 − ( − 2 ) ) 2 = 26 = 5.1 ST=\sqrt{\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}}=\sqrt{\left(\left(-1\right)-0\right)^{2}+\left(3-\left(-2\right)\right)^{2}}=\sqrt{26}=5.1 ST = ( x 1 − x 2 ) 2 + ( y 1 − y 2 ) 2 = ( ( − 1 ) − 0 ) 2 + ( 3 − ( − 2 ) ) 2 = 26 = 5.1
So, let's find perimeter now:
P = R S + R T + S T P=RS+RT+ST P = RS + RT + ST
P = 5 + 3.6 + 5.1 = 13.7 u n i t s ( n e a r e s t t e n t h ) P=5+3.6+5.1=13.7 units (nearest tenth) P = 5 + 3.6 + 5.1 = 13.7 u ni t s ( n e a res tt e n t h )
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