The perimeter of a right angled triangle is 72cm and its area is 216cm2. Find the sum of the lengths of its perpendicular sides (in cm).
36
32
42
50
A
42
B
36
C
32
D
50
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Solution
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Perimeter of right triangle = 72
a+b+c= 72 _____________ (1)
its area = 216
12ba=216
ba=432 ___________ (2)
∴c2=a2+b2 (By pythagoras theorem )
(a+b+c)2=a2+b2+c2+2ab+2bc+2ac
(72)2=c2+c2+2ab+2bc+2ac
5184=2c2+2ab+2bc+2ac
5184=2c2+2ab+2c(b+a)
5184=2c2+2ab+2c(72−c)
5184=2c2+2ab+144c−2c2
5184=2ab+144c
5184=2×432+144c
c=9320144
c=30
putting c in equation (1)
a+b+c=72
a+b=72-30
a+b=42.
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