Question

find the area of triangle whose sides measure on 20 cm 30 cm and 40 cm​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Assumption

∆PQR are the sides of triangle.

P = 20 cm

Q = 30 cm

R = 40 cm

Now,

Perimeter of ∆ = (P + Q + R)

= (20 + 30 + 40)

= 90

Semi perimeter

{\boxed{\sf\:{s=\dfrac{P+Q+R}{2}}}}

s=

2

P+Q+R

\tt{\rightarrow\dfrac{90}{2}}→

2

90

= 45 cm

Using Herons Formula

{\boxed{\sf\:{Area\;of\; \triangle=\sqrt{s(s-a)(s-b)(s-c)}}}}

Areaof△=

s(s−a)(s−b)(s−c)

\tt{\rightarrow\sqrt{45(45-20)(45-30)(45-40)}}→

45(45−20)(45−30)(45−40)

\tt{\rightarrow\sqrt{45\times 25\times 15\times 5}}→

45×25×15×5

\tt{\rightarrow\sqrt{3^2\times 5\times 5^2\times 3\times 5\times 5}}→

3

2

×5×5

2

×3×5×5

\tt{\rightarrow\sqrt{3^2\times 5^2\times 5^2\times 5\times 3}}→

3

2

×5

2

×5

2

×5×3

\tt{\rightarrow 3\times 5\times 5\sqrt{15}}→3×5×5

15

\tt{\rightarrow 75\sqrt{15}}→75

15

= 75 × 3.8729

= 290.47 cm²