Question

The sides of the triangle are in ratio 5:8:12 if
perimeter is 250m so what is the area
below are the options
$375 \sqrt{7}$
$1500 \sqrt{9}$
$852 \sqrt{4}$
$789 \sqrt{4}$




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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

.

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