Can someone help me with this problem

The measure of WZ is 16 mm.

Step-by-step explanation:

We know that:

2(PR + RS + SP) = WY + YZ + WZPR = 5 mm∠P = 37°∠S = 37°PS = 8 mmRS = 5 mmΔPRS is an isosceles triangle∠W = 37° ∠Z = 37°WY = 10 mmYZ = 10 mmΔWYZ is an isosceles triangle

We know that both triangles are isosceles because both of them have same angles on the base. Now, let's solve 2(PR + RS + SP) = WY + YZ + WZ.

2(PR + RS + SP) = WY + YZ + WZ=> 2(5 + 5 + 8) = 10 + 10 + WZ                                             [Inserting values]=> 2(18) = 20 + WZ=> 36 = 20 + WZ=> 36 - 20 = WZ=> 16 mm = WZ

Hence, the measure of WZ is 16 mm.