Paolo wrote the following equation for the perimeter of a rectangle. P=2(t+W) Which equation is equivalent to the equation Paolo wrote?

Question

asked Feb 7, 2021 52.2k views

1 Answer

Etienne Prothon · Answer 1 · 2021-02-12T20:43:23+0000

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

P=2(l+w)

Which equation is equivalent to the equation Paolo wrote?

The equivalent equations are:

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

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