Question

If the perimeter of a triangle field is 144m and ratio of the sides is 3:4:5, find the area of the field.​

Answer 1

Let the sides be 3x, 4x and 5x

Therefore,

144m = 12x

x= 12m

Therefore the three sides are,

3x = 36m

4x = 48m

5x = 60m

Area of the field,

1/2 * height * base

= 1/2 * 48m * 36m

= 864m^2

Answer 2

Given :-

• Perimeter of the triangle field = 144m

• Ratio of the sides = 3 : 4 : 5

To Find :-

• Area of the triangle field

Solution :-

Let,

First side = 3x

Second side = 4x

Third side = 5x

$\longrightarrow \sf 3x+4x+5x = 144 \\\\\longrightarrow 12x = 144 \\\\\longrightarrow\bf x = 12$

• First side = 3 × 12 = 36 m
• Second side = 4 × 12 = 48 m
• Third side = 5 × 12 = 60 m

$\boxed{\bf Area \ of \ triangle = \sqrt{s(s-a)(s-b)(s-c)}}$

$\longrightarrow \sf s = \dfrac{a+b+c}{2} \\\\\longrightarrow s = \dfrac{144}{2} \\\\\longrightarrow s = 72$

Area of the triangle field :-

$\longrightarrow \sf \sqrt{72 (72-36)(72-48)(72-60)} \\\\\longrightarrow \sqrt{72 \times 36 \times 24 \times 12 } \\\\\longrightarrow \sqrt{36 \times 2 \times 12 \times 2\times 12 } \\\\\longrightarrow \sqrt{36^2\times 2^2 \times 12 ^2 }\\\\\longrightarrow 36 \times 2 \times 12 \\\\\longrightarrow\bf 864 \ m^2$