30.
The sides of a triangle are in the ration 11:19:24 and its perimeter is
540cm. Find the area of the triangle
Answers
The area of the triangle is 10182.33 cm².
Step-by-step explanation:
The ratio of the sides of the triangle are = 11:19:24
So, let the sides of the triangle be “11x”, “19x” and “24x”.
The perimeter of the triangle = 540 cm
We know that,
The perimeter of the triangle = Sum of all sides = 11x + 19x + 24x = 54x.
∴ 54x = 540
⇒ x = 10 cm
So, the sides of the triangle are:
11x = 11 * 10 = 110 cm
19x = 19 * 10 = 190 cm
24x = 24 * 10 = 240 cm
Now,
Semi-Perimeter, s = [Perimeter of the triangle]/2 = 540/2 = 270 cm
Using Heron’s Formula, we get
Area of the triangle is,
= √[s(s-a)(s-b)(s-c)] ……. Where a, b & c are the sides of the triangle
= √[270(270-110)(270-190)(270-240)]
= √[270 * 160 * 80 * 30]
= √[103680000]
= 101823.33 cm²
Thus, the area of the triangle is 101823.33 cm².
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