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:

$w = \frac{p-2l}{2}\\\\l = \frac{p-2w}{2}\\\\p = 2l+2w$

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

$\frac{P}{2} = \frac{2(l+w)}{2}\\\\\frac{P}{2} = l + w$

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

$\frac{P}{2} - l = l + w - l\\\\\frac{P}{2} - l =w$

$w = \frac{p-2l}{2}$

Similarly solving for "l" we get,

$l = \frac{P-2w}{2}$

Also, given equation can be written as,

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

Thus the equivalent equations are found