The perimeter of a triangle is 54 m and its sides are in the ratio of 5:6 :7.The area of the triangle is

The perimeter of a triangle is 54 m and its sides are in the ratio of 5:6 :7.The area of the triangle is
1). 18 sq.m.
2). $54\sqrt{6}$ sq.m.
3). $27\sqrt{2}$ sq.m.
4). 25 sq.m.

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2 answers

35 vote

Answered by Guest on 2018-01-20 02:51:01 | Votes 35 | #

it from previous year ssc papers, $54\sqrt{6}$ sq.m. is the right answer

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Alin Malya Rashmi G · Accepted Answer · 2021-12-26 06:46:34

Solution:

Given: Perimeter of the triangle = 54 m

Ratio of the sides of the triangle = 5 : 6 : 7

Let the sides be a = 5x , b = 6x , c = 7x.

So, 5x + 6x + 7x = 54 m

18x = 54

x = 54/18

x = 3 m

So, the sides are,

a = 5(3) = 15 m

b = 6(3) = 18 m

c = 7(3) = 21 m

Heron's formula :

Area = √[S(S - a)(S - b)(S - c)] sq.units

where, S = (a + b + c)/2

S = (15 + 18 + 21)/2 = 27

Area = √[27(27 - 15)(27 - 18)(27 - 21)] m²

Area = √[27(12)(9)(6)] m²

Area = √[17496] m²

Area = 54√6 m²

So, the correct option is 2). 54√6 sq.m.

The perimeter of a triangle is 54 m and its sides are in the ratio of 5:6 :7.The area of the triangle is

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