Use the diagram to find lengths. 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. What is the length of PC?
А
B
C
PC is
cm in length.

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 = = 30 cm

BC = = 30 cm

CD = = 30 cm

Since the triangle, BPC is a right-angled triangle as 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;

= 1156

PC = 34 cm

Hence, the length of the side PC is 34 cm.