Question

Sides of a triangle 20m 34m 42m.find its area​

Answer 1

Answer:

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Find the area of the triangle whose sides are 42 cm, 34 cm and 20 cm in length. Hence, find the height corresponding to the longest side.

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Answer

Correct option is

A

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

Answer 2

Answer -

• The area of the triangle = 336 m.

To find -

• The area of the triangle.

Step-by-step explanation -

• The sides of a scalene triangle are given to us. We will find it's area using Heron's formula!

First let's find the semi-perimeter of the triangle!

We know that -

$\bigstar \: \boxed{\sf Semi-Perimeter = \dfrac{a + b + c}{2}}$

Where -

• a, b and c are the sides of the triangle.

Therefore -

$\mathfrak{\longmapsto Semi-Perimeter = \dfrac{20 + 34 + 42}{2}}$

$\mathfrak{\longmapsto Semi-Perimeter = \cancel{\dfrac{96}{2}}}$

$\mathfrak{\longmapsto Semi-Perimeter = 48 \: m}$

________________________________

• Now, let's find the area of the triangle!

Area of a scalene triangle -

$\bigstar \:\sf \sqrt{s \: (s - a) \: (s - b) \: (s - c)}$

Where -

• s = Semi-perimeter.
• a, b and c are the sides of the triangle.

Therefore -

$\tt Area = \sqrt{48 \: (48 - 20) \: (48 - 34 ) \: (48 - 42)}$

$\tt Area = \sqrt{48 \: (28) \: (14) \: (6)}$

$\tt Area = \sqrt{48 \times 28 \times 14 \times 6}$

$\tt Area = \sqrt{112896}$

$\tt Area = 336 \: m$

Hence -

• The area of the triangle is 336 m.

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