Answer:
The length of the side PC is 34 cm.
Step-by-step explanation:
We are given that BP is the perpendicular bisector of AC. QC is the perpendicular bisector of BD. AB = BC = CD.
Suppose BP = 16 cm and AD = 90 cm.
As, it is given that AD = 90 cm and the three sides AB = BC = CD.
From the figure it is clear that AD = AB + BC + CD
So, AB = [tex]\frac{90}{3}[/tex] = 30 cm
BC = [tex]\frac{90}{3}[/tex] = 30 cm
CD = [tex]\frac{90}{3}[/tex] = 30 cm
Since the triangle, BPC is a right-angled triangle as [tex]\angle[/tex]PBC = 90°, so we can use Pythagoras theorem in this triangle to find the length of the side PC.
Now, the Pythagoras theorem states that;
[tex]\text{Hypotenuse}^{2} = \text{Perpendicular}^{2} +\text{Base}^{2}[/tex]
[tex]\text{PC}^{2} = \text{BP}^{2} +\text{BC}^{2}[/tex]
[tex]\text{PC}^{2} = \text{16}^{2} +\text{30}^{2}[/tex]
[tex]\text{PC}^{2} = 256+900[/tex] = 1156
[tex]\text{PC}=\sqrt{1156}[/tex]
PC = 34 cm
Hence, the length of the side PC is 34 cm.
