Question

Sides of triangle 5:3:4 and its perimeter 720 find the area

Answer 1

EXPLANATION.

sides of triangle = 5:3:4

it's perimeter be = 720.

To find the area.

Let the sides be = 5x , 3x , 4x

=> 5x + 3x + 4x = 720

=> 12x = 720

=> x = 60

Therefore,

=> 5x = 5 X 60 = 300

=> 3x = 3 X 60 = 180

=> 4x = 4 X 60 = 240

$\sf : \implies \: s \: = \dfrac{a + b + c}{2} \\ \\ \sf : \implies \: s \: = \frac{300 + 180 + 240}{2} \\ \\ \sf : \implies \: s \: = \frac{720}{2} = 360$

$\sf : \implies \: by \: using \: herons \: formula \\ \\ \sf : \implies \: \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \sf : \implies \: \sqrt{360(360 - 300)(360 - 180)(360 - 240)} \\ \\ \sf : \implies \: \sqrt{360 \times 60 \times 180 \times 120} \\ \\ \sf : \implies \: \sqrt{466560000} \\ \\ \sf : \implies \: 21600 \: sq \: m {}^{2}$

$\sf : \implies \: \green{{ \underline{its \: area \: = 21600 \:sq \: m {}^{2} }}}$

Answer 2

Gɪᴠᴇɴ :-

• Sides of the triangle are in the ratio = 5:3:4

• Perimeter = 720

Tᴏ Fɪɴᴅ :-

• Find the area.

Sᴏʟᴜᴛɪᴏɴ :-

• Let the ratio be x.

$\sf\large\orange{★ \:5x,3x,4x}$

• Therefore,

$\sf\large\blue{⇝AB + BC + CA = 720}$

$\sf\large\blue{⇝5x + 3x + 4x = 720}$

$\sf\large\blue{⇝12x = 720}$

$\sf\large\blue{⇝x = \frac{720}{12} }$

$\sf\large\blue{⇝x = 60}$

• Now, Putting the value of x.

$\sf\large\purple{➯ AB = 5 × 60 = 300\: cm}$

$\sf\large\purple{➯ BC = 3 × 60 180\: cm}$

$\sf\large\purple{➯ AC = 4 × 60 = 240\: cm }$

• To find area :-

$\sf\large\pink{➨ S = \frac{300 + 180 + 240}{2} = \frac{720}{2} = 360 }$

$\sf\large\pink{➨ Area = \sqrt{360(360 - 300)(360 - 180)(360 - 240)} }$

$\sf\large\pink{➨ Area = 360\times60 \times 180 \times 120 }$

$\sf\large\pink{➨ Area = 466560000 }$

$\sf\large\pink{➨ Area = 21600m^{2} }$

${\boxed{{\bf{∴So,\:Area\:of\:the\:triangle = 21600m^{2}}}}}$