Question

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The sides of a triangle are in the ratio 12:17:25 and its perimeter is 540cm. Find its area?
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Answer 1

Answer:

area of triangle =l×b×h=28×27×11=5712

Answer 2

• GIVEN:-

The sides of a triangle are in the ratio 12:17:25.

Perimeter = 540 cm.

• To Find:-

Area of the triangle.

• SOLUTION:-

We know that the perimeter of a triangle is the sum of its three sides.

So,

According to the question,

$\large\therefore{\sf{Let \:the\: sides \:be \:12x,\: 17x,\: 25x}}$

$\large\Longrightarrow{\sf{12x+17x+25x=540}}$

$\large\Longrightarrow{\sf{54x=540}}$

$\large\Longrightarrow{\sf{x=\frac{540}{54}}}$

$\large\therefore\boxed{\sf{x=10}}$

So the sides are:-

12x=12×10=120 cm

17x=17×10=170 cm

25x=25×10=250 cm

• Now let's verify it:-

$\large\Longrightarrow{\sf{120+170+250=540}}$

$\large\Longrightarrow{\sf{540=540}}$

$\large\therefore\boxed{\sf{LHS=RHS}}$

$\large{\sf{Now \:its \:semiperimter \:is\: \frac{540}{2}}}$

$\large\therefore\boxed{\sf{Semiperimeter = 270}}$

Now by using Heron's Formula,

$\large\sqrt{\sf{s(s - a)(s - b)(s - c)}}$

where s is the semi perimeter and a,b,c are the three sides of the triangle.

Putting the values,

$\large\Longrightarrow{\sf{\sqrt{270(270 - 120)(270 - 170)(270 - 250)}} }$

$\large\Longrightarrow{\sf{ \sqrt{270(150 \times 100 \times 20)} }}$

$\large\Longrightarrow {\sf{\sqrt{270 \times 300000} }}$

$\large\Longrightarrow{\sf{\sqrt{81000000}}}$

$\large\therefore\boxed{\sf{9000 \: {cm}^{2} }}$

$\huge\pink\therefore\boxed{\sf{\pink{Area\: of\: triangle=9000\:{cm}^{2}}}}$