Question

Fund an expression for the perimeter of each of the following figure​

Answer 1

Answer:

5x + 6y

Step-by-step explanation:

As per the provided information in the given question, we have :

⠀⠀⠀⠀★ 1st side = x + 2y

⠀⠀⠀⠀★ 2nd side = 2x+ 3y

⠀⠀⠀⠀★ 3rd side = 2x + y

We are asked to calculate the perimeter of the triangle.

Let us denote the perimeter of this ∆ as P.

― Perimeter of the ∆ is can be measured by adding the values of all of its sides or we can say that the sum of all the sides of a triangle is its perimeter. According to the question, we have the algebraic expressions of its sides,

$\longrightarrow \sf{\quad {P = (x + 2y) + (2x + 3y) + (2x + y)}}$

Removing the brackets.

$\longrightarrow \sf{\quad {P = x + 2y + 2x + 3y + 2x + y}}$

Now, grouping all the like terms in the R.H.S.

$\longrightarrow \sf{\quad {P = x+ 2x + 2x + 2y + 3y + y}}$

Performing addition of the like terms in R.H.S.

$\longrightarrow \quad\underline{\boxed {\textbf{\textsf{P = 5x + 6y}}}}$

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

Therefore,

⠀⠀⠀⠀★ Perimeter = 5x + 6y

$\underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

Learn More!

• Perimeter of ∆ = Sum of all sides
• Sum of interior angles of a triangle = 180°
• Sum of two interior opposite angles = Exterior angle
• Area of ∆ = ½bh