Question

The area of the triangle whose sides are 42 cm, 34 cm and 20 cm in length is (a) 150 cm (b) 336 cm (c) 300 cm (d) none of these​

Answer 1

Answer:

336

Step-by-step explanation:

336 cm

2

,16 cm

Sides of the triangle are a=42,b=34,c=20

According to Hero's formula,

Area of the triangle, A=

s(s−a)(s−b)(s−c)

Where s=

2

a+b+c

=

2

42+34+20

=48

Now,

A=

48(48−42)(48−34)(48−20)

A=

48(6)(14)(28)

A=

(6×8)(6)(14)(14×2)

A=14×6×4

A=336cm

2

Let the height corresponding to longest side (42cm) is h

Area =

2

1

×base×height

2

1

×42×h=336

h=

42

336×2

=16 cm

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Answer 2

Given : The Sides of Triangle are 42 cm , 34 cm & 20 cm , respectively.

Need To Find : The Area of Triangle .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

We've the , Three Sides of Triangle ( i.e. 42 cm , 34 cm & 20 cm ) and we'll find Area of Triangle using Heron's Formula .

• For this , Firstly we need to find Semi-Perimeter (s) of the Triangle and Half of Perimeter of Triangle is called Semi-Perimeter (s) of Triangle [ i.e. ( a + b + c ) / 2 ] .

$\\ \dashrightarrow \sf s \:=\:\dfrac{ a + b + c }{2} \:\\\\\\ \dashrightarrow \sf s \:=\:\dfrac{ 42 + 34 + 20 }{2} \:\\\\\\\dashrightarrow \sf s \:=\:\cancel {\dfrac{ 96 }{2}} \:\\\\\\ \dashrightarrow \pmb {\underline {\boxed { {\:\frak{ \:s\:\:=\:48\:cm\:}}}}}\:\bigstar \:$

∴ Semi-Perimeter (s) of Triangle is 48 cm .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

$\qquad \bigstar \:\underline {\:\pmb{\sf\: Using\:Heron's \:Formula \:To\:Find\:Area\:of\:\triangle \:\::\:}}$

$\qquad \star\:\underline {\boxed {\pmb{\sf\:Area_{\:(Triangle)}\:=\: \sqrt{ \:\:s\:\Big(\: s - a \:\Big)\:\Big(\:s - b\:\Big)\:\Big(\:s - c\:\Big)\:}\:}}}$

where :

• s is the Semi-Perimeter of Triangle ( i.e. 48 cm )
• a , b & c are Three sides of Triangle.
• Given Sides of Triangle are 42 cm , 34 cm & 20 cm .

$\\\qquad \dag\:\underline {\frak{Substituting \:Known \:Values \:in\:Given \:Formula \:\::\:}}\:$

$\twoheadrightarrow \sf Area_{\:(Triangle)}\:=\: \sqrt{ \:\:s\:\Big(\: s - a \:\Big)\:\Big(\:s - b\:\Big)\:\Big(\:s - c\:\Big)\:}\:\\\\\\ \twoheadrightarrow \sf Area_{\:(Triangle)}\:=\: \sqrt{ \:\:48\:\Big(\: 48 - 42 \:\Big)\:\Big(\:48 - 34\:\Big)\:\Big(\:48 - 20\:\Big)\:}\:\\\\\\ \twoheadrightarrow \sf Area_{\:(Triangle)}\:=\: \sqrt{ \:\:48\:\times 6 \times 14 \times 28 \:}\:\\\\\\ \twoheadrightarrow \sf Area_{\:(Triangle)}\:=\: \sqrt{ \:\:288 \times 392 \:}\:\\\\\\ \twoheadrightarrow \sf Area_{\:(Triangle)}\:=\: \sqrt{ \:112896 \:}\:\\\\\\\twoheadrightarrow \pmb {\underline {\boxed {\pink {\:\frak{ \:336\:cm^2\:}}}}}\:\bigstar \:$

∴ Hence, Area of Triangle is Option b) 336 cm² .