Saved Bookmarks
| 1. |
The perimeter of a triangle is 540 m and its sides are in the ratio 12 : 25 : 17. Find the areaof the triangle. Please show proper steps |
|
Answer» Answer: Let the sides of the TRIANGLE be 12a,25a,17a. We KNOW that PERIMETER of the triangle = SUM of all sides $$ ⇒12a+25a+17a=54a Given, perimeter of the triangle =540m ⇒54a=540m a=10m So, the lengths of the sides of triangle are 12a=120m 25a=250m 17a=170m We can use HERON's formula to get the area of triangle Area of triangle with sides with sides a,b,c and semiperimeter s= s(s−a)(s−b)(s−c)
. and s= 2 a+b+c
For triangle with sides 120 m, 250 m and 170 m, s= 2 120+250+170
=270m Substituting the sides 120 m, 250 m and 170 m in the Heron's formula, we get 270(270−120)(270−250)(270−170)
= 270×150×20×100
= 9×30×30×5×20×20×5
=3×30×5×20 =9000m 2 |
|