Question

The diagram below shows the rectangle BOAR B Find the length o fsegment PA . if entering your answer as a decimal, round your final answer to the nearest hundredth

Answer 1

Answer:

4.62 units

Step-by-step explanation:

Let's first find the length OR.

OR² = BR² + OB²

OR² = 5² + 12²

OR² = 25 + 144

OR² = 169

$OR = \sqrt{19}$

OR = 13

Let's find the area of triangle OBR.

Using the formula :

½bh

Where

b = BR

h = OB

Therefore, area of triangle OBR =

½ * BR * OB

= ½ * 5 * 12

= 30

From the diagram, triange OBR and OAR are parallel to each other, and they equal.

Thus, area of OBR = area of OAR

To find the length PA, we have :

Area of OAR = ½ * OR *PA

Let's make PA subject of the formula:

$PA = \frac{area of OAR}{\frac{1}{2} * OR}$

$PA = \frac{30}{\frac{1}{2} * 13}$

PA = 4.618 ≈ 4.62

PA = 4.62 units