What is the perimeter of triangle with vertices of (1,2) (3,-4)(1,2)(3,−4) and (-4,5)(−4,5)?

1 Answer
Shwetank Mauria
Feb 28, 2016

Perimeter is 23.55823.558

Explanation:

To find the perimeter of a triangle with vertices of (1,2)(1,2), (3,−4)(3,−4) and (−4,5)(−4,5), we have to first find distance between each pair of points, which will give length of sides. For this we use distance formula between two points (x_1,y_1)(x1,y1) and (x_2,y_2)(x2,y2) is sqrt((x_2-x_1)^2+(y_2-y_1)^2)√(x2−x1)2+(y2−y1)2. Hence if lengths of sides are L_1,L_2,L_3L1,L2,L3, these are as follows:

L_1=sqrt((3-1)^2+((-4)-(2))^2)=sqrt(2^2+(-6)^2)=sqrt(4+36)=sqrt40=2sqrt10=6.325L1=√(3−1)2+((−4)−(2))2=√22+(−6)2=√4+36=√40=2√10=6.325

L_2=sqrt((-4-(3))^2+(5-(-4))^2)=sqrt((-7)^2+9^2)=sqrt(49+81)=sqrt130=11.402L2=√(−4−(3))2+(5−(−4))2=√(−7)2+92=√49+81=√130=11.402

L_3=sqrt((-4-1)^2+(5-2)^2)=sqrt((-5)^2+3^2)=sqrt(25+9)=sqrt34=5.831L3=√(−4−1)2+(5−2)2=√(−5)2+32=√25+9=√34=5.831

Hence Perimeter is 6.325+11.402+5.831=23.5586.325+11.402+5.831=23.558

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