Question

if the sides of a triangle are in the ratio 3:5:7 and its perimeter is 300 m. Find its area (i) 100√2 (ii) 500√2 (iii) 1500√3 (iv) 200√3​

Answer 1

Answer:

Correct option is iii)1500√3 m²

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= 60+100+140/2

= 300/2

=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 m²

Hence, area of the triangular plot is 1500√3 m²

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Answer 2

Answer: The area of the triangle is $1500\sqrt{3} m^{2}$

Step-by-step explanation:

Let the three sides of triangle be 3x , 5x , 7x.

given, perimeter = 300 m

therefore, $3x + 5x + 7x = 300\\ 15x = 300\\ x = 300/15\\ x = 20$

therefore, sides of the triangle are:

$3 * 20 = 60\\5 * 20 = 100\\7 * 20 = 140$

to find area of the triangle,

$s = 300/2\\s = 150$

therefore, area of triangle =

$= \sqrt{s*(s-a)*(s-b)*(s-c)} , \\\\= \sqrt{150*(150-60)*(150-100)*(150-140)} \\=\sqrt{150*90*50*10}\\=\sqrt{10*15*10*9*10*5*10)}\\\\=100*\sqrt{15*9*5}\\=100*\sqrt{3*5*3*3*5}\\=100*15\sqrt{3} \\=1500\sqrt{3} m^{2}$