1. The length of the sides of a tri...
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1. The length of the sides of a triangle are in the ratio 3:4:5 and its perimeter is 144 cm. The area of the triangle is (1) 684 cm (2) 664 cm? (3) 764 cm2 (4) 864 cm?

11th - 12th Class
Maths
Solution
269
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Length of the sides of a triangle are 3: 4: 5 ratio [ text { Perimeter }=144 mathrm{cm} ] let ( x ) be the common facter of the ratio [ begin{array}{c} 3 x+4 x+5 x=144 12 x=144 x=12 end{array} ] the sides are [ 3 x>4 x, 5 x ] ite 36,48,60 cms. Area of ( Delta=sqrt{s(s-a)(s-b)(s-c)} ) where ( s ) is ene semi-perimeter and ( a, b, c ) are the sidas [ begin{aligned} therefore text { Area } &=sqrt{72(72-36)(72-48)(72-60)} &=sqrt{72 times 36 times 24 times 12} &=sqrt{frac{36 times 2 times 36 times 12 times 2 times 12}{-12}} &=frac{436 times 2 times 12}{864 mathrm{cm}^{2}} text { option }-(4) end{aligned} ]
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