Question

find the area of the triangle whose sides measure 52 CM, 56 cm and 60 CM respectively.

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

★Assumption :-

a = 52 cm

b = 56 cm

c = 60 cm

★We know that :-

★Perimeter of triangle

= (a + b + c)

= (52 + 56 + 60) cm

= 168 cm

★Now :-

$\tt{\rightarrow s=\dfrac{1}{2}(a+b+c)}$

$\tt{\rightarrow s=\dfrac{1}{2}\times 168}$

= 84 cm

(s - a) = (84 - 54)

= 32 cm

(s - b) = (84 - 56)

= 28 cm

(s - c) = (84 - 60)

= 24 cm

★Using Heron's Formula :-

$\tt{\rightarrow\sqrt{s(s-a)(s-b)(s-c)}}$

$\tt{\rightarrow\sqrt{84\times 32\times 28\times 24}}$

$\tt{\rightarrow\sqrt{14\times 6\times 16\times 2\times 14\times 2\times 6\times 4}}$

$\tt{\rightarrow\sqrt{14\times 6\times 4\times 2\times 2}}$

= 1344 cm²

Answer 2

✿━━━━@♥ℳg━━━━✿

$\boxed{Explained\:Answer}$

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✿━━━━@♥ℳg━━━━✿

$\mathfrak{\huge{\pink{ANSWER}}}$

Here , we will use Heron's formula for calculating the area of the triangle.

Let the sides of triangle be a, b and c, where

a = 52 cm,

b = 56 cm,

c = 60 cm

Perimeter = 2S = a + b + c

=>               2S = 52+56+60 = 168 cm

=>        S = 168/2 = 84 cm

As per Heron's formula

Area of triangle = √s(s-a)(s-b)(s-c) 

                          = √84(84-52)(84-56)(84-60)

                   = √84(32)(28)(24)

= √1806336

= 1344 cm2.

                   

  Area of triangle = 1344 cm2