# The formula for the perimeter of a triangle is p=2L+2W what is the formula for W?

Nov 5, 2015

$W = \text{p-2L"/"2}$

#### Explanation:

Any mathematical equation can be modified as to isolate a single variable. In this case, you would like to isolate $W$

The first step is to subtract $2 L$ from each side, by the subtraction property of equality, like so:
$p = 2 L + 2 W$
$- 2 L | - 2 L$

This leaves you with:
$p - 2 L = 0 + 2 W$ or $p - 2 L = 2 W$, simplified.

When a variable has a coefficient like $2 W$, it means that you are multiplying the coefficient by the variable. The reverse of multiplication is division which means to get rid of the 2, we simply divide each side by 2, by the division property of equality, like so:
$\text{p-2L"/"2"="2W"/"2}$ or $\text{p-2L"/"2"=W}$, simplified.

By the symmetric property of equality, we can flip this equation around to say:
$W = \text{p-2L"/"2}$