The perimeter of a right angled triangle is 144cm and its hypotenuse measures 65cm. Find the lengths of the other sides and calculate its area.

Asked by Shibu.charly | 10th Aug, 2015, 11:41: PM

Expert Answer:

L e t space o n e space s i d e space o f space t h e space r i g h t space t r i a n g l e space b e space a. I t space i s space g i v e n space t h a t space h y p o t e n u s e space m e a s u r e s space 65 space c m. S o space t h e space o t h e r space s i d e space o f space t h e space t r i a n g l e space m e a s u r e s space square root of 65 squared minus a squared end root. A l s o space g i v e n space t h a t space p e r i m e t e r space o f space t h e space t r i a n g l e space i s space 144 T h u s comma space w e space h a v e comma a plus square root of 65 squared minus a squared end root plus 65 equals 144 rightwards double arrow square root of 65 squared minus a squared end root equals 144 minus a minus 65 rightwards double arrow square root of 65 squared minus a squared end root equals 79 minus a S q u a r i n g space b o t h space t h e space s i d e s comma space w e space h a v e comma 65 squared minus a squared equals open parentheses 79 minus a close parentheses squared rightwards double arrow 65 squared minus a squared equals 79 plus a squared minus 2 cross times 158 cross times a rightwards double arrow 4225 minus a squared equals 6241 minus 4225 plus a squared minus 158 cross times a rightwards double arrow 2 a squared minus 158 a plus 2016 equals 0 rightwards double arrow a squared minus 79 a plus 1008 equals 0 rightwards double arrow a squared minus 63 a minus 16 a plus 1008 equals 0 rightwards double arrow a open parentheses a minus 63 close parentheses minus 16 open parentheses a minus 63 close parentheses equals 0 rightwards double arrow open parentheses a minus 16 close parentheses open parentheses a minus 63 close parentheses equals 0 rightwards double arrow a minus 16 equals 0 space o r space a minus 63 equals 0 rightwards double arrow a equals 16 space o r space a equals 63 O n e space s i d e space o f space t h e space t r i a n g l e space i s space 16 space c m space a n d space t h e space o t h e r space s i d e space o f space t h e space t r i a n g l e space i s space 63 space c m. A r e a equals 1 half cross times 16 cross times 63 equals 504 space c m squared

Answered by Vimala Ramamurthy | 11th Aug, 2015, 09:16: AM