The length of the two sides of a right triangle containing the right angle differ by 2 cm. if the area of the triangle is 24cm sq, find the perimeter of the triangle.

Asked by eeshan.nk | 6th Aug, 2016, 10:12: PM

Expert Answer:

begin mathsize 16px style L e t space t h e space t r i a n g l e space b e space A B C space r i g h t minus a n g l e d space a t space B.
T h e n comma space l e t space t h e space l e n g t h space o f space A B equals x space c m
rightwards double arrow space l e n g t h space o f space B C equals left parenthesis x minus 2 right parenthesis space c m
N o w comma space a r e a space o f space t r i a n g l e A B C equals 1 half cross times A B cross times B C
rightwards double arrow 24 equals 1 half cross times x cross times left parenthesis x minus 2 right parenthesis
rightwards double arrow 48 equals x squared minus 2 x
rightwards double arrow x squared minus 2 x minus 48 equals 0
rightwards double arrow x squared minus 8 x plus 6 x minus 48 equals 0
rightwards double arrow x left parenthesis x minus 8 right parenthesis plus 6 left parenthesis x minus 8 right parenthesis equals 0
rightwards double arrow left parenthesis x minus 8 right parenthesis left parenthesis x plus 6 right parenthesis equals 0
rightwards double arrow x minus 8 equals 0 space o r space x plus 6 equals 0
rightwards double arrow x equals 8 space o r space x equals negative 6
rightwards double arrow x equals 8 space c m space equals space A B
rightwards double arrow x minus 2 equals 8 minus 2 equals 6 space c m space equals space B C
N o w comma space t h i r d space s i d e comma space A C equals square root of A B squared plus B C squared end root equals square root of 64 plus 36 end root equals 10 space c m
H e n c e comma space p e r i m e t e r equals A B plus B C plus A C equals 8 plus 6 plus 10 equals 24 space c m end style

Answered by Rashmi Khot | 8th Aug, 2016, 10:15: AM