The perimeter of a right angle …
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Gaurav Seth 4 years, 4 months ago
Let a,b, c are the sides of a triangle .
Given that hypotenuse(c) = 26 cm.
a + b + c = 60 cm.
∴ a + b = 60 - c = 60 - 26 =
∴ a + b = 34 --------(1)
In a right angled triangle c2 = a2 + b2
a2 + b2 = 262 = 676 ---------(2)
Now a2 + ( 34 - a)2 = 676. [ from (1)]
⇒ a2 + a2 - 68a + 1156 = 676
⇒ 2a2 - 34a + 480 = 0
⇒ a2 - 17a + 240 = 0
⇒ a2 - 10a - 24a + 240 = 0
⇒ a(a - 10) - 24(a - 10) = 0
∴ a = 10 , 24
but b = 34 - a then b = 24 , 10
∴ sides of triangle are 10 , 24.
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