Question

1. A circular play area with radius 3 m is to be
partitioned into two sections using a straight
fence as shown in the figure. How long should
the fence be?​

Answer 1

Answer:

6m

Step-by-step explanation:

As the fence is dividing the park into two sections using a straight line it will be the diameter.

2r=d

2(3)= 6

Answer 2

Note: the image mentioned in the question is attached in the answer.

Given: radius of the circle is 3 m.

To find: the length of the fence.

Solution:

Draw the required figure.

Write the equation of the circle.

$\[\begin{array}{l}{x^2} + {y^2} = {r^2}\\ \Rightarrow {x^2} + {y^2} = {3^2}\\ \Rightarrow {x^2} + {y^2} = 9 - - - - - - \left( 1 \right)\end{array}\]$

Observe that from the given figure, that the fence is passing through the point $(-1,0)$.

Substitute in equation (1).

$\[\begin{array}{l}{x^2} + {y^2} = 9\\ \Rightarrow {\left( { - 1} \right)^2} + {y^2} = 9\\ \Rightarrow 1 + {y^2} = 9\end{array}\]$

$\[\begin{array}{l} \Rightarrow {y^2} = 8\\ \Rightarrow y = \pm 2\sqrt 2 \end{array}\]$

Hence, the length of the fence is,

$\[2 \times 2\sqrt 2 = 4\sqrt 2 cm\]$