Question

Tʜᴇ ᴛᴡᴏ sɪᴅᴇs ᴏғ ᴀ ᴛʀɪᴀɴɢᴜʟᴀʀ ғʟᴀɢ ᴀʀᴇ 30 ᴄᴍ ᴀɴᴅ 40 ᴄᴍ. Fɪɴᴅ ᴛʜᴇ ʟᴇɴɢᴛʜ ᴏғ ᴛʜᴇ ᴛʜɪʀᴅ sɪᴅᴇ ɪғ ᴛʜᴇ ᴘᴇʀɪᴍᴇᴛᴇʀ ᴏғ ᴛʜᴇ ғʟᴀɢ ɪs 130 ᴄᴍ ?​

Answer 1

Answer:

Given :-

The two sides of a triangular flag are 30 cm and 40 cm.

The perimeter of the flag is 130 cm.

To Find :-

What is the length of the third side of a triangular flag.

Formula Used :-

$\clubsuit$ Perimeter Of Triangle Formula :

$\footnotesize\mapsto \sf\boxed{\bold{\pink{Perimeter_{(Triangle)} =\: Sum\: Of\: All\: Sides}}}$

Solution :-

Let,

$\mapsto \bf Third\: Side_{(Triangular\: Flag)} =\: y\: cm$

Given :

First Side (a) = 30 cm

Second Side (b) = 40 cm

Third Side (c) = y cm

According to the question by using the formula we get,

$\footnotesize\bigstar\: \: \sf\bold{\purple{Perimeter_{(Triangular\: Flag)} =\: Sum\: Of\: All\: Sides}}$

$\longrightarrow \bf Perimeter_{(Triangular\: Flag)} =\: a + b + c$

By putting a = 30 cm, b = 40 cm and c = y cm we get,

And,

Perimeter = 130 cm

$\longrightarrow \sf 130 =\: 30 + 40 + y$

$\longrightarrow \sf 130 =\: 70 + y$

$\longrightarrow \sf 130 - 70 =\: y$

$\longrightarrow \sf 60 =\: y$

$\longrightarrow \sf\bold{\red{y =\: 60\: cm}}$

Hence, the third side of a triangular flag is :

$\leadsto \sf Third\: Side_{(Triangular\: Flag)} =\: y\: cm$

$\leadsto \sf\bold{\red{Third\: Side_{(Triangular\: Flag)} =\: 60\: cm}}$

${\small{\bold{\underline{\therefore\: The\: length\: of\: third\: side\: of\: a\: triangular\: flag\: is\: 60\: cm\: .}}}}$

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

★ VERIFICATION ★

As we know that :

$\footnotesize\bigstar\: \: \sf\boxed{\bold{\blue{Perimeter_{(Triangle)} =\: Sum\: Of\: All\: Sides}}}$

Given :

Perimeter = 130 cm

$\implies \sf 130 =\: 30 + 40 + y$

By putting y = 60 cm we get,

$\implies \sf 130 =\: 30 + 40 + 60$

$\implies \sf 130 =\: 70 + 60$

$\implies \bf 130 =\: 130$

Hence, Verified.

Answer 2

Step-by-step explanation:

Let third side be x cm.

Perimeter of triangle = 120

40+30+x=120

70+x=120

x=120-70=50 cm

Now we see that (50)^2=(40)^2+(30)^2

So it is a rightangle triangle whose base and perpendicular are 40cm and 30cm respectively.

So we needn't to use heron formula to calculate the area of triangle.

Area of a right angle triangle =(base×perpendicular)/2=(30×40)/2=1200/2=600 sq. cm

Hope it will help you.