Question

Use the diagram to find lengths. BP is the perpendicular bisector of AC. QC is the

Answer 1

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 = $\frac{90}{3}$ = 30 cm

BC = $\frac{90}{3}$ = 30 cm

CD = $\frac{90}{3}$ = 30 cm

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

$\text{Hypotenuse}^{2} = \text{Perpendicular}^{2} +\text{Base}^{2}$

$\text{PC}^{2} = \text{BP}^{2} +\text{BC}^{2}$

$\text{PC}^{2} = \text{16}^{2} +\text{30}^{2}$

$\text{PC}^{2} = 256+900$ = 1156

$\text{PC}=\sqrt{1156}$

PC = 34 cm

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