MATH SOLVE

3 months ago

Q:
# The length of ZX is 2 units. What is the perimeter of triangle XYZ? 5 + + 2 units5 + 3 units5 + + 2 units10 + 2 units

Accepted Solution

A:

Keywordstriangle,perimeter,distance, length, side, pointswe know thatThe perimeter of a triangle is the sum of the three length sideTo find the length side calculate the distance between two pointsThe formula to calculate the distance between to points is equal to [tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Step 1Find the distance ZY[tex]Z(1,0)\\Y(3,1)[/tex] substitute the values

[tex]d=\sqrt{(1-0)^{2}+(3-1)^{2}}[/tex]

[tex]dZY=\sqrt{5}\ units[/tex]

Step 2Find the distance XY[tex]X(-1,4)\\Y(3,1)[/tex] substitute the values

[tex]d=\sqrt{(1-4)^{2}+(3+1)^{2}}[/tex]

[tex]dXY=\sqrt{25}=5\ units[/tex] Step 3Find the perimeter of the triangle[tex]P=ZX+ZY+XY[/tex]we have[tex]dZX=2\sqrt{5}\ units[/tex]

[tex]dZY=\sqrt{5}\ units[/tex]

[tex]dXY=5\ units[/tex] Substitute[tex]P=(2\sqrt{5}+\sqrt{5}+5)\ units[/tex]thereforethe answer is [tex]P=(3\sqrt{5}+5)\ units[/tex]

Step 1Find the distance ZY[tex]Z(1,0)\\Y(3,1)[/tex] substitute the values

[tex]d=\sqrt{(1-0)^{2}+(3-1)^{2}}[/tex]

[tex]dZY=\sqrt{5}\ units[/tex]

Step 2Find the distance XY[tex]X(-1,4)\\Y(3,1)[/tex] substitute the values

[tex]d=\sqrt{(1-4)^{2}+(3+1)^{2}}[/tex]

[tex]dXY=\sqrt{25}=5\ units[/tex] Step 3Find the perimeter of the triangle[tex]P=ZX+ZY+XY[/tex]we have[tex]dZX=2\sqrt{5}\ units[/tex]

[tex]dZY=\sqrt{5}\ units[/tex]

[tex]dXY=5\ units[/tex] Substitute[tex]P=(2\sqrt{5}+\sqrt{5}+5)\ units[/tex]thereforethe answer is [tex]P=(3\sqrt{5}+5)\ units[/tex]