Question

the perimeter of a triangular field is 144 and ratio of their sides is 3 is to 4 is to 5 find area of the field​

Answer 1

Answer:

3x + 4x + 5x = 144

12x = 144

x = 144/12

x = 12

using heron's formula

area = 864

Answer 2

Step-by-step explanation:

Total perimeter = 144

Ratio = 3:4:5

Let sides be

$3x \\ 4x \\ 5x$

So,

$3x + 4x + 5x = 144 \\ 12x = 144 \\ x = 12$

First side =

$3(12) = 36$

Second side =

$4(12) = 48$

Third side =

$5(12) = 60$

Area is found by Heron's formula

$\sqrt{s(s - a)(s - b)(s - c)} \\ s = \frac{a + b + c}{2} \\ s = \frac{36 + 48 + 60}{2} \\ s = \frac{144}{2} = 72$

Area =

$\sqrt{72(72 - 36)(72 - 48)(72 - 60)} \\ \sqrt{72 \times 36 \times 24 \times 12 } \\ = 864 \: sq.units$