Question

side of a triangular field are in ratio 5 3 and 4 it can be fenced once with a 36 M long wire find the area of field​

Answer 1

Step-by-step explanation:

let the sides be-

5x, 3x and 4x

Total perimeter = 36m

So, 5x + 3x + 4x = 36

12x = 36

x = 3

Hence the sides are-

5 × 3 = 15

3 × 3 = 9

4 × 3 = 12

For area of the field, Apply Heron's formula -

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

where,

$s \: = \:( a + b + c ) \div 2$

So, s = (15+9+12)÷2 = 36÷2 = 18

Area =

$\sqrt{18(18 - 15)(18 - 9)(18 - 12)}$

=

$\sqrt{18 \times 3 \times 9 \times 6}$

=

$\sqrt{2916}$

= 54 sq m