Question

Can you please help me with number 2? i’m confused thanks

Answer 1

Question 2.

Given:

• QR = 5

,

• PT = 4

Let's find the perimeter of the quadilateral PQRS.

Here, the radius of the circle is 5 units.

Thus, we have:

TR = 5

RS = 5

PR = PT + TR = 4 + 5 = 9

Now, apply the tangent - radius theorem which states that the angle between a tangent a radius is a right angle.

To find the lengths of PQ and QS, apply Pythagorean Theorem:

`\begin{gathered} PR^2=PQ^2+QR^2 \\ \\ PQ^2=PR^2-QR^2 \end{gathered}`

Where:

PR = 9

QR = 5

Thus, we have:

`\begin{gathered} PQ^2=9^2-5^2 \\ \\ PQ^2=81-25 \\ \\ PQ^2=56 \\ \\ PQ=\sqrt[]{56} \\ \\ PQ=\sqrt[]{14*4} \\ \\ PQ=\sqrt[]{14*2^2} \\ \\ PQ=2\sqrt[]{14} \end{gathered}`

Now, using the two tangents theorem which states that two tangents whcih meet at the same point are equal in length.

We have:

PQ = PS = 2√14

To find the perimeter of quadilateral PQRS, apply the formula:

Perimeter = QR + RS + PQ + PS

Input the values and evaluate:

`\begin{gathered} \text{Perimeter}=5+5+(2\sqrt[]{14})+(2\sqrt[]{14}) \\ \\ \text{Perimeter}=10+4\sqrt[]{14} \end{gathered}`

Therefore, the perimeter of the quadilatral is:

`10+4\sqrt[]{14}`

ANSWER: B

`10+4\sqrt[]{14}`