Question

perimeter of an triangle is 28 m there side are 4m,16m,x .find x​

Answer 1

ANSWER = 8m

EXPLANATION

We know that, Perimeter of a triangle =

(sum of all sides)

First side of triangle = 4 m

Second side of triangle = 16 m

Third side = x

(4 + 16 + x)m = 28

= (20 + x)m = 28

= x = 28 - 20

= x = 8

So, the third side of the traingle is 8 m

(Hope it will help u)

Answer 2

Clarification:

Here,in the question we are given that perimeter of the triangle is 28 m. And we are also given that its sides are 4m , 16 m and x. We have to find out measure of unknown side (x).

In order to find the measure of unknown side, we'll form a suitable linear equation and will take the third side as variable (x). Then by transposition method, we'll find its unknown side.

Given:

• Perimeter of triangle = 28 m

• Sides = 4 m , 16 m & x

To calculate:

• Measure of unknown side (x)

Calculation:

As we know that,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\star \: \: {\underline {\boxed {\large {\sf \red { {Perimeter}_{(\triangle)} = Sum \: of \: all \: sides } }}}} \\ \\ \\ \sf{ \longrightarrow \: 28 \: m = 4 \:m \: + 16m + x} \\ \\ \\ \sf{ \longrightarrow \: 28 \: m = 20 \: m + x} \\ \\ Transposing \: 20 \: from \: RHS \: to \: LHS - \\ \\ \\ \sf{ \longrightarrow \: 28 \: m - 20 \: m = x} \\ \\ \\ \longrightarrow \: \underline{\boxed{\sf{8 \: m = x}}} \: \red{\bigstar}$

Henceforth, measure of unknown side (x) is 8 m.

Verification :

$\boxed{ \mathbf{LHS}} \\ \\ \leadsto \: \rm{Perimeter \: of \: triangle} \\\leadsto \: \rm{28 \: m} \\ \\ \\ \boxed{ \mathbf{RHS}} \\ \\ \leadsto \: \rm{sum \: of \: all \: sides} \\\leadsto \: \rm{4 \: m + 16m + \sf \red{x \: m}} \\ \leadsto \: \rm{4 \: m + 16m + \sf \red{8 \: m}} \\ \leadsto \: \rm{28\: m }$

LHS = RHS

Hence, verified!!

More !!

Important properties of triangle :

★ Angle sum property of a triangle :

• Sum of interior angles of a triangle = 180°

★ Exterior angle property of a triangle :

• Sum of two interior opposite angles = Exterior angle

★ Perimeter of triangle :

• Sum of all sides

★ Area of triangle :

• $\sf { \dfrac{1}{2} \times Base \times Height }$

★ Area of an equilateral triangle:

• $\sf { \dfrac{\sqrt{3}}{4} \times {Side}^{2} }$

★ Area of a triangle when its sides are given :

• $\sf { \sqrt{s[ (s-a)(s-b)(s-c) ]} }$

Where,

• S= Semi-perimeter or $\sf {\dfrac{a+b+c}{2} }$