Question

see the attachment....... ​

Answer 1

ㅤ$\;\;\underline{\textbf{\textsf{ Given :-}}}$

• Distance between the two inner parallel line segments is = 60 m

(They are each 106m long)

• Wide of the track is = 10 m

ㅤ$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• The distance around the track along its inner edge.

ㅤ$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

Let the radius of inner semi-circle be r.

Then,

$\leadsto {\sf{ 2r = 60m}}$

$\leadsto {\sf{ r = \frac{60}{2} m}}$

$\leadsto {\sf{ r = 30m}}$

ㅤ$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\underline{\textsf{ The radius of inner semi-circle is \textbf{ 30 m }}}.$

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Again :-

$\boxed{\sf{ Distance \: around \: the \: edge \: along \: its \: inner \: edge = AB+ BC + CD + DA}}$

$\leadsto {\sf{ 106m + \pi \: \times 30m + 106m + \pi \times 30m}}$

$\leadsto {\sf{ 212m + 2 \times \frac{22}{7} \times 30m }}$

$\leadsto {\sf{ 212m + \frac{1320}{7} m}}$

$\leadsto {\sf{ \frac{1484 + 1320}{7} m}}$

$\leadsto {\sf{ \frac{2804}{7} m}}$

ㅤ$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\underline{\textsf{The distance around the track along its inner edge is \textbf{ 400.57m }}}.$

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