Question

The perimeter of triangle is 84cm and it's area 336 cm^2 CM. if one side measure 30cm find the other two side.

Answer 1

Sol: 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.

Answer 2

Answer:

Step-by-step explanation

Semi-perimeter = 84/2 = 42 cm.

Perimeter = 84 cm. Let a = 30 cm then b+c = 54. c = 54-b. Area = 336 cm^2 given

By Heron's formula

Area = √(s)(s-a)(s-b)(s-c)

=> 336 = √(42)(42–30)(42-b){42–(54-b)}

=> 336 = √(42)(12)(42-b)(b-12)

=> 336 = 6√(7)(2)(42-b)(b-12)

=> 56 = √14(-b^2 +54b -504)

=> (56)(56) = 14 (-b^2 +54b -504)

=> 224 = -b^2 +54b -504

=> b^2 -54b +728 = 0

=> b= 26 or b= 28

If b= 26, c= 54-b = 28

If b= 28, c= 54-b = 26

So the other two sides are 26 cms and 28 cms.

Hope that it helps you