Question

perimeter of a triangle is 84cm, one side is 30cm and area is 336cm².find other two sides​

Answer 1

Answer:

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 cm and 28 cm