Question

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}
]

# 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?

Solution