Question

The perimeter of a triangler field is 540m
and its sides are in the Ratio 25:17. 12 find the area
of the triangle
​

Answer 1

♧QUESTION♧

The perimeter of a triangler field is 540m

and its sides are in the Ratio 25:17:12. Find the area

of the triangle.

♧SOLUTION♧

GIVEN

PERIMETER = 540 m

RATIO = 25 : 17 : 12

FORMULA

PERIMETER = SIDE + SIDE + SIDE

LET THE RATIOS BE THE MULTIPLE OF 'x'

Then,

The numbers will be 25x , 17x , 12x

ACCORDING TO QUESTION

$Perimeter = side + side + side$

$=> 540 = 25x + 17x + 12x$

$=> 540 = 54x$

$=>\frac{540}{54} = x$

$=> 10 = x$

REQUIRED ANGLES:-

$25x = 25 × 10 = 250m$

$17x = 17 × 10 = 170$

$12x = 12c× 10$

TO FIND THE AREA

FORMULA :

BY USING HERON'S FORMULA

a = 250 , b = 170 , c = 120

$s = \frac{a + b + c}{2}$

$s = \frac{250 + 170 + 120}{2}$

$s = \frac{540}{2}$

$s = 270$

Therefore, semi perimeter = 270m

Now,

$A = \sqrt{s(s-a)(s-b)(s-c)}$

$A = \sqrt{270(270-250)(270-170)(270-120)}$

$A = \sqrt{270× 20× 100× 150}$

$A = \sqrt{81000000}$

$A = 9000m²$

THEREFORE

AREA OF TRIANGLE = 9000m²

HOPE THIS ANSWER WILL YOU!!