Question

the sides of the best triangle are in the ratio of 12 to 17 is 25 and its perimeter is 540 cm find its area​

Answer 1

☆ ǫᴜᴇsᴛɪᴏɴ :-

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

☆ ᴛᴏ ғɪɴᴅ :-

• The area of triangle

☆sᴏʟᴜᴛɪᴏɴ :-

Let,

The sides of the triangle be 12x, 17x, 25x.

So,

The required formula is Perimeter of triangle = a + b + c

540 = 12x + 17x + 25x

540 = 54x

x = $\frac{540}{54}$

x = 10

Therefore, x = 10

a = 12x = 12 × 10 ⇨120cm

b = 17x = 17 × 10 ⇨ 170cm

c = 25x = 25 × 10 ⇨ 250cm

So,The required formula for area is Area of triangle = $\sqrt{s(s - a)(s - b)(s - c)}$

2S = 540

S = 540/2 = 270

Applying the values by the given formula,

$= \sqrt{270(270 - 120)(270 - 170)(270 - 250)} {cm}^{2}$

$= \sqrt{270(150)(100)(20)} {cm}^{2}$

$= 9000 \: {cm}^{2}$

Hence,The area of triangle is 9000 cm^2.

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