Question

find the perimeter of a rectangle where length and breadth are given by 3x + 10 & 5x + 7 ​

Answer 1

Step-by-step explanation:

perimeter of Rectangle= 2( length+ breadth)

=2(3 x +10 + 5x + 7)

=2(8x + 17)

=16x + 34

Answer 2

${\underline {\boxed {\large {\bf \gray { Perimeter = (16x + 34) \: units } }}}}$

Clarification :

Here, we are given a question from the topic Algebraic Expressions. We are given that the length of the rectangle is (3x + 10) units and breadth of the rectangle is (5x + 7) units. We have to find the perimeter of rectangle.

We'll basically use here the formula of perimeter of rectangle to find the perimeter of the rectangle. By using the formula, we'll perform the multiplication and addition of polynomials.

Explication of steps :

Given,

• Length of the rectangle = (3x + 10) units

• Breadth of the rectangle = (5x + 7) units

To calculate,

• Perimeter of the rectangle.

Calculation,

As we know that,

$\bigstar \: \boxed{\sf { {Perimeter}_{(Rectangle)} = 2 ( \ell + b)}}$

• $\ell$ denotes length.
• b denotes breadth.

Substituting values,

$\longrightarrow$ Perimeter = 2 [ ( 3x + 10 ) + ( 5x + 7 ) ] units

• Removing brackets.

$\longrightarrow$ Perimeter = 2 (3x + 10 + 5x + 7) units

• Grouping like terms.

$\longrightarrow$ Perimeter = 2 (3x + 5x + 10 + 7) units

• Peforming addition.

$\longrightarrow$ Perimeter = 2 (8x + 17) units

• Using distributive property.

$\longrightarrow$ Perimeter = 2(8x) + 2(17) units

• Performing multiplication.

$\longrightarrow$ Perimeter = 16x + 34 units

$\underline{\boxed{\sf{ Perimeter_{(Rectangle)} = (16x + 34) \: units }}} \: \red{\bigstar}$

Therefore, perimeter of the rectangle is (16x + 34) units.

A little further...!

More about rectangles :

1. A rectangle is a quadrilateral having 4 side, 4 angles and 4 vertices.
2. Opposite sides of a rectangle are equal.
3. Opposite angles of a rectangle are equal.
4. It is a parallelogram.
5. Its opposite sides are parallel to each other.
6. Diagonals of a rectangle bisect each other.
7. Perimeter of rectangle = 2 ( l + b )
8. Area of rectangle = Length × Breadth