Question

Four horses are tethered with equal ropes at 4 corners of a square field of side 35 metres so that they just can reach one another. Find the area left ungrazed by the horses​

Answer 1

$\red{\textbf{Answer :-}}$$232.5{m}^{2}$

Step-by-step explanation:

$\red{\textbf{Given :-}}$

$\textsf{Side of a square = 35 m}$

$\textsf{Also, }$

$\textsf{four horses are tethered with equal}$

$\textsf{ropes at 4 corners of the square field.}$

$\textsf{Hence, }$

$\textsf{each horse can graze up to 35 m of distance along the side.}$

$\textsf{Therefore, the area of the square field =}$

$\textsf{side×side = 35×35 }$

$= 1225 {m}^{2}$

$\textsf{The grazed area is making a complete}$

$\textsf{circle by taking all the four grazed parts.}$

$\textsf{So, the area of grazed part = }$

$\pi {r}^{2} = \Large \frac{22}{7} \small \times 17.5 \times 17.5$

$= 992.5{m}^{2}$

$\textsf{Ungrazed area left = area of square field-}$

$\textsf{area of grazed part}$

$\textsf{= 1225 -992.5}$

$= 232.5{m}^{2}$

$\textsf{so ,the area left ungrazed by the horses, }$

$= 232.5{m}^{2}$.