Question 1006063
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The sides of a triangle are in the ratio 5:12:13 and its perimeter is 150 m. Find the area of triangle.
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This phrase "The sides of a triangle are in the ratio 5:12:13" means that there exists 
a segment of some length d which is the common measure of the triangle sides such that

  the first side of the triangle has the length 5d,

  the second side of the triangle has the length 12d, and 

  the third side of the triangle has the length 13d.

Then the perimeter of the triangle is 5d + 12d + 13d = 30d = 150 m

Hence d= {{{150/30}}} = 5 m.

Now you can find the measures of the triangle sides. They are

5d = 5*5 = 25 m, 12d = 12*5 = 60 m and 13d = 13*5 = 65 m.

Now notice that 

{{{13^2}}} = {{{5^2 + 12^2}}} = {{{169}}}, 

and it implies that

{{{(13d)^2}}} = {{{(5d)^2 + (12d)^2}}}.

It means that the given triangle is a right-angled triangle with the legs of 5d = 25 m and 12d = 60 m.

Finally, you can calculate the area of the triangle. It is half the product of its legs, {{{1/2}}}.25*60 = 750 {{{m^2}}}.

<U>Answer</U>. Area of the triangle is 750 {{{m^2}}}.
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