Question

What is the perimeter of WXYZ?

Answer 1

Answer:

48

Step-by-step explanation:

If the follows triangle congruence, you look at the two triangles given.

Triangle XYZ is equiangular due to it's 3 congruent angles.

Since Triangle XYZ is equiangular, that means it is also equilateral, meaning each side is congruent.

This means that side XY and Side ZY are equal to XZ and therefore

XY = 11 and ZY = 11.

Then we look at Triangle WXZ. Triangle WXZ has two congruent base angles, meaning it's an isosceles triangle.

By the converse of the isosceles triangle theorem, if 2 angles of a triangle are congruent then the sides opposite those angles are congruent.

This means XZ and WZ are congruent to each other, meaning XZ = WZ.

Since XZ= 11, that means WZ = 11.

Now we have all outside side lengths and we can find the perimeter.

Perimeter = WX + WZ + ZY + XY.

(substitute known values of sides)

11+11+11+15= Perimeter

33+15 = Perimeter

48 = Perimeter