Question

the perimeter of a triangle is 60cm .its hypotenuse is 26 cm, find the other two sides and the area of the triangle.​

Answer 1

Answer:

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.