Question

The length of ZX is 2 units. What is the perimeter of triangle XYZ?

Answer 1

Answer:B:   5+3square root of 5 units

Step-by-step explanation:just took the test

Answer 2

Keywords

triangle,perimeter,distance, length, side, points

we know that

The perimeter of a triangle is the sum of the three length side

To find the length side calculate the distance between two points

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

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

Step 1

Find the distance ZY

$Z(1,0)\\Y(3,1)$  

substitute the values

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

$dZY=\sqrt{5}\ units$

Step 2

Find the distance XY

$X(-1,4)\\Y(3,1)$  

substitute the values

$d=\sqrt{(1-4)^{2}+(3+1)^{2}}$

$dXY=\sqrt{25}=5\ units$  

Step 3

Find the perimeter of the triangle

$P=ZX+ZY+XY$

we have

$dZX=2\sqrt{5}\ units$

$dZY=\sqrt{5}\ units$

$dXY=5\ units$  

Substitute

$P=(2\sqrt{5}+\sqrt{5}+5)\ units$

therefore

the answer is

$P=(3\sqrt{5}+5)\ units$