Final answer:
To find the area of a triangle with sides in ratio 12:17:26 and perimeter 540 cm, we can use Heron's formula. By multiplying each ratio by a common multiplier and solving for the value of x, we find the lengths of the sides to be 120 cm, 170 cm, and 260 cm. Using Heron's formula, we calculate the area of the triangle to be 44325 cm².
Step-by-step explanation:
To find the area of a triangle, we can use Heron's formula. First, we need to find the lengths of the sides of the triangle. Let's assume the ratio of the sides is 12:17:26. If we multiply each ratio by a common multiplier, we get 12x:17x:26x. Then, we can set up an equation to find the value of x. Since the perimeter of the triangle is 540 cm, we have 12x + 17x + 26x = 540. Solving for x, we get x = 10. Substituting the value of x back into the ratios, we find that the lengths of the sides are 120 cm, 170 cm, and 260 cm. Now, we can use Heron's formula to find the area of the triangle. The formula is A = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (s = (a+b+c)/2) and a, b, and c are the lengths of the sides. Plugging in the values, we have s = (120 + 170 + 260)/2 = 275 cm. Then, A = √(275(275-120)(275-170)(275-260)) = √(275(155)(105)(15)) = √(1968753750) = 44325 cm².