Question

ASAP Please.What is the perimeter of triangle ABC? Round each step to the nearest tenth. Enter your answer in the box.

Answer 1

Answer:

The perimeter of triangle ABC  is 15.8 units

Step-by-step explanation:

we know that

The perimeter of a triangle is equal to the sum of its three length sides

$P=AB+BC+AC$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have the coordinates

$A(5,-1),B(-1,1),C(0,-3)$

step 1

Find the distance AB

we have

$A(5,-1),B(-1,1)$

substitute in the formula

$d=\sqrt{(1+1)^{2}+(-1-5)^{2}}$

$d=\sqrt{(2)^{2}+(-6)^{2}}$

$d_A_B=\sqrt{40}\ units$

$d_A_B=6.3\ units$

step 2

Find the distance BC

we have

$B(-1,1),C(0,-3)$

substitute in the formula

$d=\sqrt{(-3-1)^{2}+(0+1)^{2}}$

$d=\sqrt{(-4)^{2}+(1)^{2}}$

$d_B_C=\sqrt{17}\ units$

$d_B_C=4.1\ units$

step 3

Find the distance AC

we have

$A(5,-1),C(0,-3)$

substitute in the formula

$d=\sqrt{(-3+1)^{2}+(0-5)^{2}}$

$d=\sqrt{(-2)^{2}+(-5)^{2}}$

$d_A_C=\sqrt{29}\ units$

$d_A_C=5.4\ units$

step 4

Find the perimeter

$P=AB+BC+AC$

substitute the values

$P=6.3+4.1+5.4$

$P=15.8\ units$