Question

Three horses trthered with 7m long rope at three corners

Of a triangular field having the sides 21m, 21√2m and 21m.

Find the area of the field on which each horse can graze.​

Answer 1

Answer:

ꜱᴄɪᴇɴᴄᴇ, ᴀɴʏ ꜱʏꜱᴛᴇᴍ ᴏꜰ ᴋɴᴏᴡʟᴇᴅɢᴇ ᴛʜᴀᴛ ɪꜱ ᴄᴏɴᴄᴇʀɴᴇᴅ ᴡɪᴛʜ ᴛʜᴇ ᴘʜʏꜱɪᴄᴀʟ ᴡᴏʀʟᴅ ᴀɴᴅ ɪᴛꜱ ᴘʜᴇɴᴏᴍᴇɴᴀ ᴀɴᴅ ᴛʜᴀᴛ ᴇɴᴛᴀɪʟꜱ ᴜɴʙɪᴀꜱᴇᴅ ᴏʙꜱᴇʀᴠᴀᴛɪᴏɴꜱ ᴀɴᴅ ꜱʏꜱᴛᴇᴍᴀᴛɪᴄ ᴇxᴘᴇʀɪᴍᴇɴᴛᴀᴛɪᴏɴ. ɪɴ ɢᴇɴᴇʀᴀʟ, ᴀ ꜱᴄɪᴇɴᴄᴇ ɪɴᴠᴏʟᴠᴇꜱ ᴀ ᴘᴜʀꜱᴜɪᴛ ᴏꜰ ᴋɴᴏᴡʟᴇᴅɢᴇ ᴄᴏᴠᴇʀɪɴɢ ɢᴇɴᴇʀᴀʟ ᴛʀᴜᴛʜꜱ ᴏʀ ᴛʜᴇ ᴏᴘᴇʀᴀᴛɪᴏɴꜱ ᴏꜰ ꜰᴜɴᴅᴀᴍᴇɴᴛᴀʟ ʟᴀᴡꜱ. ꜱᴄɪᴇɴᴄᴇ.

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Answer 2

Step-by-step explanation:

Given,

Three horses trthered with 7m long rope at three corners of a triangular field having the sides AB= 21m, BC= 21m and AC=21√2m respectively.

To find:- The area of the field on which each horse can graze.

solution:-

In ∆ABC we have,

=> (AB)² +( BC)² = (AC)² [ Pythagoras theorem]

=> (21)² +( 21)² = (21√2)²

=> 441 + 441 = 441 × 2

=> 882. = 882.

So, From the above it is clear that ∆ABC is a Right isosceles triangle.

By angle sum property:

Angles ( CAB + ACB + ABC ) = 180°

x° + x° + 90° = 180°

2x° +90°= 180°

x° = 45°

Now,

The area of the field on which the horse at A and B can graze = π r² x°

360°

= 2/7 × 7× 7 × 45°

360°.

= 22×7× 45°

360°

= 19.25 m²

The area of the field on which horse at B can graze = π r² 90°

360°

= 2/7 × 7× 7 × 90°

360°.

= 22×7× 90°

360°

= 38.5 m².

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