Question

the perimeter of right angled triangle is 60cm it's hypothesis is 26cm find area

Answer 1

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.
So now area =1/2*24*10=120 cm²