Question

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

Answer 1

Answer:

Area Of Triangle = $750 \: \: m$

Step-by-step explanation:

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See The Attachment My Friend....

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Answer 2

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

The sides of a triangle are in the ratio 5:12:13 and it's perimeter is 150 m.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The area of the triangle.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the ratio of the side of triangle be r

• 5r
• 12r
• 13r

We know that formula of the perimeter of triangle :

$\boxed{\bf{Perimeter=side+side+side}}}}}$

A/q

$\longrightarrow\sf{5r+12r+13r=150}\\\\\longrightarrow\sf{30r=150}\\\\\longrightarrow\sf{r=\cancel{\dfrac{150}{30} }}\\\\\\\longrightarrow\sf{\purple{r=5\:m}}$

$\bullet\sf{1_{st}\:side\:of\:\triangle=5r=(5\times 5)m=\boxed{\sf{25m}}}}\\\bullet\sf{2_{nd}\:side\:of\:\triangle=12r=(12\times 5)m=\boxed{\sf{60m}}}}\\\bullet\sf{3_{rd}\:side\:of\:\triangle=13r=(13\times 5)m=\boxed{\sf{65m}}}}$

$\underline{\underline{\bf{Using\:Heron's\:formula\::}}}}}$

We have 3 side :

a = 25 m , b = 60 m and c = 65 m

$\longrightarrow\tt{Semi-perimeter=\dfrac{Sum\:of\:side}{2} }\\\\\\\longrightarrow\tt{Semi-perimeter=\dfrac{a+b+c}{2} }\\\\\\\longrightarrow\tt{Semi-perimeter=\dfrac{25m+60m+65m}{2} }\\\\\\\longrightarrow\tt{Semi-perimeter=\cancel{\dfrac{150}{2}} m}\\\\\\\longrightarrow\tt{\purple{Semi-perimeter=75\:m}}$

Now;

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

$\mapsto\tt{Area\:_{triangle}=\sqrt{75(75-25)(75-60)(75-65)}} \\\\\mapsto\tt{Area\:_{triangle}=\sqrt{75(50)(15)(10)}} \\\\\mapsto\tt{Area\:_{triangle}=\sqrt{562500} }\\\\\mapsto\tt{\purple{Area\:_{triangle}=750\:m^{2} }}$

Thus;

$\dag\underbrace{\sf{The\:area\:of\:triangle=750\:m^{2} }}}}$