Question

Paolo wrote the following equation for the perimeter of a rectangle.

P=2(t+W)
Which equation is equivalent to the equation Paolo wrote?

Answer 1

Question:

Paolo wrote the following equation for the perimeter of a rectangle.

P=2(l+w)

Which equation is equivalent to the equation Paolo wrote?

Answer:

The equivalent equations are:

`w = (p-2l)/(2)\\\\l = (p-2w)/(2)\\\\p = 2l+2w`

Solution:

Given that:

The equation for perimeter of rectangle written by Paolo is:

P = 2(l + w)

where

l = length side of rectangle

w = width side of the rectangle

We have to find the equivalent equation

Let us solve the equation for "w"

`P = 2(l + w)`

Divide by 2 both sides

`(P)/(2) = (2(l+w))/(2)\\\\(P)/(2) = l + w`

`\text{Subtract L on both sides of equation }`

`(P)/(2) - l = l + w - l\\\\(P)/(2) - l =w`

`w = (p-2l)/(2)`

Similarly solving for "l" we get,

`l = (P-2w)/(2)`

Also, given equation can be written as,

`P = 2(l+w)\\\\P = 2l + 2w`

Thus the equivalent equations are found