Question

The length of ZX is 2 units. What is the perimeter of triangle XYZ? 5 + + 2 units 5 + 3 units 5 + + 2 units 10 + 2 units

Answer 1

B

Explanation:

Answer 2

B) 5 + 3√5 units

Step-by-step explanation:

The length of ZX is 2√5 units. What is the perimeter of triangle XYZ?

A) 5 +√3 + 2 √5 units

B) 5 + 3√5 units

C) 5 + √6 + 2√5 units

D) 10 + 2√5 units

From the diagram attached, point X is at (-1, 4), Y(3, 1), Z(1, 0).

The distance between two point

`O(x_1,y_1)\ and\ A(x_2,y_2)\ is\ given\ as:\\\\OA=√((y_2-y_1)^2+(x_2-x_1)^2)`

The lengths of the sides of the triangle are:

`|XY| = √((3-(-1))^2+(1-4)^2)=√(25) =5\ unit\\ \\|XZ|= √((1-(-1))^2+(0-4)^2)=√(20) =2√(5) \ unit\\\\|YZ|= √((1-3)^2+(0-1)^2)=√(5) \ unit`

The perimeter of the triangle is the sum of all the sides, i.e.

Perimeter = |XY| + |YZ| + |XZ| = 5 + 2√5 + √5 = 5 + 3√5