Question

How can I find the perimeter of rectangle

Answer 1

Let's consider what the question asks for:

--> perimeter of a rectangle

To find the perimeter of the rectangle:

--> we need to know the side length

Let's consider how to find our side length:

--> in a rectangle

--> opposite parallel sides are equal in length

--> in a mathematical equation, we get:

`4x-4y=3x+5y\\2-2y=x-3y`

Now we notice,

--> in the second equation, there is only one 'x'

--> therefore if we find a y-value to substitute into the 'x'

--> we can solve

Let's use the first equation to see how 'x' and 'y' relate to each other:

`4x-4y=3x+5y\\4x-3x=4y+5y\\x=9y`

Let's use that x-value and plug it the second equation:

`2-2y=x-3y\\2-2y=(9y)-3y\\2-2y=6y\\2=8y\\\\y=(1)/(4)`

Since x = 9y:

`x=9y=9*(1)/(4) =(9)/(4)`

Let's find each side length:

`4x-4y=4((9)/(4)) -4((1)/(4) )=9-1=8\\\\2-2y=2-2((1)/(4) )=2-(1)/(2) =(3)/(2) =1.5\\\\3x+5y=3((9)/(4))+5((1)/(4) )=(27)/(4) +(5)/(4) =(32)/(4)=8\\ \\x-3y=(9)/(4) -3((1)/(4))=(9)/(4)-(3)/(4) =(6)/(4) =1.5`

Let's add up the side length to find the perimeter:

`\text{Perimeter}=8+1.5+8+1.5=9.5+9.5=19`

Answer: 19

Answer 2

The perimeter of any figure is the total distance required to form the shape’s edges. So, in a rectangle, the perimeter is the sum of all side lengths, since this is the distance required to form the rectangle’s sides.

The formula for perimeter of a rectangle is:

P=2L+2W, where P=perimeter, L=length, and W=Width

The formula is simplified from:

P=L+L+W+W, since the perimeter of any figure is the sum of all side lengths, and rectangles have 2 pairs of opposite, congruent sides.

Now, substitute the Length and Width into the formula. Remember, length is how long the rectangle is; it is the measurement of how far it extends. The width is how wide the rectangle is; it is the measurement of how far out the rectangle extends.

Now, let’s substitute the expressions into the formula. We won’t use P=2L+2W because we have different expressions for each dimension.

P=[(4x-4y)+(3x+5y)]+[(x-3y)+(2-2y)]

Combine like terms using the associative property of addition:

P=[(4x+3x)+(-4y+5y)] +[(x-3y +(2-2y)]

Combine like terms:

P=(7x+y)+(x-3y)+(2-2y)

P=(7x+y)+(x+2)+(-3y-2y)

P=(7x+y)+(x+2)+(-5y)

P=(7x+x)+(y-5y)+2

P=8x-4y+2