Question #270003

The vertices of a triangle are R (3,0), S (-1,3), and T (0, -2). a) Classify the triangle by side length and b) Find the perimeter of the triangle to the nearest tenth.

1
Expert's answer
2021-11-24T10:30:28-0500

R (3,0), S (-1,3), and T (0, -2)

RS=(x1x2)2+(y1y2)2=(3(1))2+(03)2=25=5RS=\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

RT=(x1x2)2+(y1y2)2=(30)2+(02)2=13=3.6RT=\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

ST=(x1x2)2+(y1y2)2=((1)0)2+(3(2))2=26=5.1ST=\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


So, let's find perimeter now:

P=RS+RT+STP=RS+RT+ST

P=5+3.6+5.1=13.7units(nearesttenth)P=5+3.6+5.1=13.7 units (nearest tenth)


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