Question

The sides of a Triangle are in the ratio 11 19:24 and

Answer 1

Answer:  The area of the triangle with the perimeter of 540 cm is approximately 10200 cm²

More exactly: 10182 cm²

Step-by-step explanation:  $A=\frac{bh}{2}$

240 × 84.85  = 10182

To get the height of the triangle, it takes some trigonometry;

Given 3 sides of a triangle, it is possible to calculate the angles using the Law of cosines and the formula $cos A =\frac{b^{2} +c^{2} -a^{2} }{2bc}$

We will need the measure of angle A, then use the sine of A to get the height of the line from angle C perpendicular to the base, side b.

We can use the dimensions given in the proportions and then multiply by 10 because the sides given add to a perimeter of 54, one tenth of the 540 cm of the actual triangle. The angles of the similar triangles are congruent.

side a = 19, side b = 24, side c = 11

24² + 11² - 19²   is   576 + 121 - 361 = 336

2(24)(11) = 528

cos A = 336 / 528  that is  0.636364$\cos^{-1}\left(.6363634\right)$= 50.47°

sin(50.47) = 0.77129

0.77129 × 11 = 8.48 is the height  Rounding to 8.5 would be reasonable for this height

Using rounded values here to calculate Area :

85 × 240/2 = 10200 cm²