Question

the perimeter of a triangle is 156 m . two sides of triangle are 48m and 30 m. find the length of the 3rd side.

Answer 1

Answer:

The length of the third side of a triangle is 78m.

Step-by-step explanation:

We are given that, the perimeter of a triangle is 156m and two sides of triangle are 48m and 30m respectively.

With this information, we are asked to find out the length of the third side of a triangle.

We know that, the sum of all sides of a triangle is equal to the perimeter of a triangle.

$\boxed{\bf{Perimeter_{(triangle)} = a + b + c}}$

Let us consider that, the length of the third side of a triangle be $c$ m.

Now, on substituting the given values in the formula, we get:

$\implies 156 = 48 + 30 + c \\\\\\ \implies 156 = 78 + c \\\\\\ \implies c = 156 - 78 \\\\\\ \implies \boxed{\bf{c = 78}}$

Hence, the length of the third side of a triangle is 77m.

$\rule{300}{2}$

Verification:

We know that, the sum of all sides of a triangle is equal to the perimeter of a triangle.

$\boxed{\bf{Perimeter_{(triangle)} = a + b + c}}$

By substituting the known values in the formula, we get:

$\implies 156 = 48 + 30 + 78 \\\\\\ \implies 156 = 78 + 78 \\\\\\ \implies \boxed{\bf{156 = 156}}$

We can see that, here both the conditions are satisfied, i.e., LHS = RHS.

Hence, verified!

Answer 2

Answer:

Given :-

• The perimeter of a triangle is 156 m.
• The two sides of a triangle are 48 m and 30 m.

To Find :-

• What is the length of the 3rd side.

Solution :-

Let,

$\implies \bf 3^{rd}\: Side_{(Triangle)} =\: c\: cm$

Given :

• Perimeter = 156 m
• First Side = 48 m
• Second Side = 30 m

According to the question by using the formula we get,

$\footnotesize \implies \sf\bold{\purple{Perimeter_{(Triangle)} =\: Sum\: Of\: All\: Sides}}$

$\footnotesize \implies \bf Perimeter_{(Triangle)} =\: 1^{st}\: Side + 2^{nd}\: Side + 3^{rd}\: Side$

$\implies \sf Perimeter_{(Triangle)} =\: a + b + c$

$\implies \sf 156 =\: 48 + 30 + c$

$\implies \sf 156 =\: 78 + c$

$\implies \sf 156 - 78 =\: c$

$\implies \sf 78 =\: c$

$\implies \sf\bold{\green{c =\: 78\: m}}$

Hence, the third side of a triangle is :

$\dashrightarrow \sf 3^{rd}\: Side_{(Triangle)} =\: c\: m$

$\dashrightarrow \sf\bold{\red{3^{rd}\: Side_{(Triangle)} =\: 78\: cm}}$

$\small \sf\bold{\underline{\blue{\therefore\: The\: length\: of\: 3^{rd}\: side\: of\: triangle\: is\: 78\: m\: .}}}$

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