a parallelogram has two sides 16cm and 25 cm and the diagonal is 65m long .find the area of the parallelogram

Asked by gauravbhardwaj65950 | 25th Apr, 2020, 09:45: PM

Expert Answer:

The question should be: A parallelogram has two sides 60cm and 25 cm and the diagonal is 65m long. Find the area of the parallelogram.

Diagonal of a parallelogram divides it into two triangles of equal area.
Length of sides of each triangle are a = 60 cm, b = 25 cm and c = 65 cm
Semiperimeter=(60+25+65)/2=150/2=75 cm
 
Area space of space each 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
equals square root of 75 open parentheses 75 minus 60 close parentheses open parentheses 75 minus 25 close parentheses open parentheses 75 minus 65 close parentheses end root
equals square root of 75 cross times 15 cross times 50 cross times 10 end root
equals square root of 5 squared cross times 3 cross times 5 cross times 3 cross times 5 squared cross times 2 cross times 5 cross times 2 end root
equals square root of 5 to the power of 6 cross times 3 squared cross times 2 squared end root
equals 5 cubed cross times 3 cross times 2
equals 750 space cm squared
Area space of space parallelogram equals 2 cross times Area space of space triangle equals 1500 space cm squared

Answered by Renu Varma | 25th Apr, 2020, 11:51: PM