Archive
7th of September 2015
Mathematics
Q:

35cm, 54cm and 61cm are the sides of a tiangle . find the length of the longest and the shortest altitudes

Mehak Srivastava - CBSE - Class IX

Monday, September 07, 2015 at 18:03:PM

A:

Hibegin mathsize 14px style Perimeter space of space given space triangle space equals space 35 plus 54 plus 61 equals 150 space cm Semi space perimetr space of space triangle space equals space 150 over 2 equals 75 space cm. If space straight s space is space the space semi space perimetr space of space increment space whose space sides space are space straight a comma space straight b space and space straight c Area space of space triangle space equals space square root of straight s open parentheses straight s minus straight a close parentheses open parentheses straight s minus straight b close parentheses open parentheses straight s minus straight c close parentheses end root therefore Area space of space given space triangle space equals space square root of 75 open parentheses 75 minus 35 close parentheses open parentheses 75 minus 54 close parentheses open parentheses 75 minus 61 close parentheses end root therefore Area space of space given space triangle space equals space square root of open parentheses 75 cross times 40 close parentheses open parentheses 21 close parentheses open parentheses 14 close parentheses end root space equals 939 space cm squared Area space of space triangle space equals 1 half cross times base cross times height The space longest space altitude space space is space on space the space shortest space side space of space triangle therefore Area space of space triangle space equals space 1 half cross times 35 space cross times height space open parentheses longest space altitude close parentheses therefore 939 space equals space 35 over 2 cross times longest space altitude therefore Longest space altitude space equals space fraction numerator 939 cross times 2 over denominator 35 end fraction equals 1878 over 35 equals 53.65 space cm The space shortest space altitude space space is space on space the space longest space side space of space triangle therefore Area space of space triangle space equals space 1 half cross times 61 space cross times height space open parentheses shortest space altitude close parentheses therefore 939 space equals space 61 over 2 cross times shortest space altitude therefore Shortest space altitude space equals space fraction numerator 939 cross times 2 over denominator 61 end fraction equals 1878 over 61 equals 38.78 space cm end style

Monday, September 07, 2015 at 18:29:PM