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Q.

The in-radius of a triangle whose sides are given by 3, 5, 6 is?


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a

https://lh5.googleusercontent.com/WYWV4ivrWymsnF-MNOkprZw9HUGDfULJRRkzhjGbV4zuYAkGDlNKmrX7Ej9yr7f8-7bXaezvSk9Our5PJ0TkG4Kif_ipK51m6_64CatSmcACwvhKY0ibHpFjM7deCbhTAjS6kLV7C1RGJHhvulyMKw

b

https://lh6.googleusercontent.com/CNNYHfqA42MBgtZ8wrHK3ai7zsLNU53hL1OtkJxvj3oZrby4ouH1z2Kk_gFpj_dTCDH1QM4uDiM0RQOrj7-2y9hR0ptwKrkAoMFDbYsExQ56TDxuyCkNDe7msFYRwlSN-9ZejmIulmn0pu3SXKi9gQ

c

https://lh3.googleusercontent.com/7_bUQr8BsURUMCcKrzBgIEqPeG_D5EgiMH9Ez1h1ZclAqrFZNIMjbOQVoebe3ucmWl7dQu5oBtvv3dz8klHWuJpBTGiW3xr1JDSxoJFo7EkmccKFzKqvlAJ01FaYq_XvOn4mao4QMcWgaWI7niEYVQ

d

https://lh6.googleusercontent.com/VwVC2v91k1S91BULMiE_NoINpNzQQsxVqoFVLF8TAXJdDrAcQV6eAL-vleXBCsio7Z_rcizN8WDSAl2u-xk8WJAQPEwqanmjj-Eqxk2P0p5u_yL_ncf34NMWSHERKAmm5Jt_aYLms7YkWe0MxMMoaA 

answer is A.

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Detailed Solution

Concept: Inradius means radius inscribed by a circle.
Inradius of a triangle is the radius inscribed by the largest circle that fits the triangle.
Area of triangle can be calculated by:
https://lh6.googleusercontent.com/rOqqcCatZDtUzmTOe5NDGDuyNvAiU15JHsJPDI7fAh7MS1kTQL2R5r3SNnJ6cwR_mekGFWt0JJPb1jO6cENtS9yfKRCs0dne3QNFxidrt_j2wtP3YNqyq7z2gDLefZoP2ycrUCe97wPk0lSWStDgQga, b and c are sides of a triangle.
s is semi perimeter.
https://lh4.googleusercontent.com/Dr7o4rT7IyYJ5btWjTX3TzNnF6Ss4ukoQ94lYbDgmsG5ZiLfNamLWnzj3sOZXkdfG9Ji12kc2sxu9a_Uho67kzcZYoxcEJuV5GCZD62bzLE3bSp3lL8-j_bwQvbU8Gajldeusad8Jfw2pINxyafP7Ahttps://lh3.googleusercontent.com/FXsurLx4dnuHreNvuq1pACGmFnPJJQeLdDJaCk51Mjmys_Rs7h6B25WRTdFoVRdrUnZ-tSgktGoq2UF2R-xEQ3wAu4Zdw4Bx-f8p7O2AD1yfuEpGXaTbUN8PHZubfYTTvcp7h2J2A2qjIxGS3696oghttps://lh6.googleusercontent.com/_6hn207UQ2czYaEsiDK4dNbLRNmJD3sOG_CCjeomjrXnKEo4HWlBqVHcdJCfC-G3VVsn42-4m-OGTZRa3INHI0bzFLBwgh1FisULvASTSvEIouqd4PHGb9DYP-y-tGEWYk0voqvlhhJ6eW-aK_3Oswhttps://lh6.googleusercontent.com/TnloGFu6cYtjnQY_sfwdxbb9Ipv21PRJ6fMuRvyBlGCzlKBZOH5hij6pB-t0aNtzR_CzIZa5iCIsobUB5KSYHaMv30z60qnLcksCEACCOO7bNE-MUtoxbuwEHQfaoeoplKvc0YRWNh5kPNGIZL8-lAHence, the correct answer is option 1) https://lh5.googleusercontent.com/WYWV4ivrWymsnF-MNOkprZw9HUGDfULJRRkzhjGbV4zuYAkGDlNKmrX7Ej9yr7f8-7bXaezvSk9Our5PJ0TkG4Kif_ipK51m6_64CatSmcACwvhKY0ibHpFjM7deCbhTAjS6kLV7C1RGJHhvulyMKw 
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