The sides of a triangle are in the ratio 5 : 12 : 13,
Question:

The sides of a triangle are in the ratio 5 : 12 : 13, and its perimeter is 150 m. Find the area of the triangle

 

Solution:

Let the sides of a triangle be 5x m ,12x m and 13x m.

Since, perimeter is the sum of all the sides,

$5 x+12 x+13 x=150$

$\Rightarrow 30 x=150$

or, $x=\frac{150}{30}=5$

The  lengths of the sides are:

$a=5 \times 5=25 \mathrm{~m}$

$b=12 \times 5=60 \mathrm{~m}$

 

$c=13 \times 5=65 \mathrm{~m}$

Semiperimeter $(\mathrm{s})$ of the triangle $=\frac{\text { Perimeter }}{2}=\frac{25+60+65}{2}=\frac{150}{2}=75 \mathrm{~m}$

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{75(75-25)(75-60)(75-65)}$

$=\sqrt{75 \times 50 \times 15 \times 10}$

$=\sqrt{562500}$

 

$=750 \mathrm{~m}^{2}$

 

 

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