Question

Find the area of a triangle, two sides of which are 40 cm and 24 cm, and perimeter is 96 cm.​

Answer 1

Given: Two sides of a triangle is 40 cm and 24 cm. Also, it's perimeter is given as 96 cm.

Need to find: Area of the triangle?

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So, we will use Heron's Formula to find the Area of Triangle (let's say ∆ABC).

✇ If the perimeter of given triangle is 96 cm then the semi perimeter of the triangle would be 48 cm. i.e ( s ) = 48 cm.

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( I ) Finding third side :

» As We know that, Perimeter of triangle is equal to sum of all sides of triangle. & The perimeter is Given that is 96 cm. Therefore:

$\\:\implies\quad\bold{{Perimeter}_{(Triangle)}=a+b+c}$

$\\\\\qquad\quad:\implies\quad\sf{96=40+24+c}$

$\\\\\qquad\qquad\quad:\implies\quad\sf{96=64+c}$

$\\\\\qquad\qquad\qquad\:\implies\quad\sf{96-64=c}$

$\\\\\qquad\qquad\qquad\qquad:\implies\quad\sf{32=c}$

Hence, third side of the triangle is 32 cm.

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( ll ) Area of the Triangle :

$\star\: \large{\underline{\boxed{\pmb{\sf{{Area}_{(Triangle)}=\sqrt{s(s-a)(s-b)(s-c)}}}}}}$

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Here,

• a = 40 cm
• b = 24 cm
• c = 32 cm
• s = 48 cm

$\\\\:\implies\quad\sf{{Area}_{(Triangle)}=\sqrt{48(48-40)(48-24)(48-32)}}$

$\\\\:\implies\quad\sf{{Area}_{(Triangle)}=\sqrt{48\times 8\times 24\times 16}}$

$\\\\:\implies\quad\sf{{Area}_{(Triangle)}=\sqrt{384\times 384}}$

$\\\\:\implies\quad\underline{\boxed{\pmb{\frak{{Area}_{(Triangle)}=\pink{384\: {cm}^{2}}}}}}\: \bigstar$

$\\\therefore\underline{\sf{Hence,\: the\: area\: of\: the\: triangle\: is\: 384\: {cm}^{2}}}$

Answer 2

Answer:

Step-by-step explanation:

let the sides of the triangle be a, b and c.

a=40 (given)

b=24(given)

a+b+c=96(given)

therefore, c = 32 (=96-24-40)

area = $\sqrt{s(s-a)(s-b)(s-c)}$

where s = (a+b+c)/2 = 48

area = $\sqrt{48(48-32)(48-40)(48-24)}$

= $\sqrt{48.8.24.16}$

=384 cm sqaure.