Question

The sides of a triangular plot are in the ratio 3:4:5 and its perimeter is 24 m. Then the area of triangular plot is​

Answer 1

Step-by-step explanation:

The sides of a the triangular plot are in the ratio 3:5:7. So, let the sides of the triangle be 3x, 5x and 7x.

Also it is given that the perimeter of the triangle is 300 m therefore,

3x+5x+7x=300

15x=300

x=20

Therefore, the sides of the triangle are 60,100 and 140.

Now using herons formula:

S=

2

60+100+140

=

2

300

=150 m

Area of the triangle is:

A=

s(s−a)(s−b)(s−c)

=

150(150−60)(150−100)(150−140)

=

150×90×50×10

=

6750000

=1500

3

m

2

Hence, area of the triangular plot is 1500

3

m

2

.

Answer 2

$\huge {\underline {\underline \pink{ƛƝƧƜЄƦ}}}$

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

$\bf Perimeter = 3x + 4x + 5x$

$\bf \implies 24m = 12x$

$\bf \implies 12x = 24m$

$\bf \implies x = 24 \div 12$

$\bf \implies x = 2m$

Therefore, Sides are :-

• 3x = 3 × 2 = 6m
• 4x = 4 × 2 = 8m
• 5x = 5 × 2 = 10m

Let a = 6m, b = 8m and c = 10m

Semi Perimeter( s ) = 24 ÷ 2 = 12m

Heron's Formula

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

$\bf \sqrt{12(12 - 6)(12 - 8)(12 - 10)}$

$\bf \sqrt{12 \times 6 \times 4 \times 2}$

$\bf \sqrt{576}$

$\bf 24m$

Therefore, Area of triangle is 24m.