If the length of each side of a triangle is doubled, how many times greater will the perimeter be?

To determine how many times greater the perimeter of a triangle becomes when the length of each side is doubled, we start by understanding the formula for the perimeter of a triangle. The perimeter (P) is the sum of the lengths of all three sides.

Let's say the original lengths of the sides of the triangle are (a), (b), and (c). The original perimeter (P) can be expressed as:

[

P = a + b + c

]

If we double the length of each side, the new lengths will be (2a), (2b), and (2c). The new perimeter (P_{\text{new}}) is calculated as follows:

[

P_{\text{new}} = 2a + 2b + 2c

]

We can factor out the 2 from the equation:

[

P_{\text{new}} = 2(a + b + c) = 2P

]

This indicates that the new perimeter is twice the original perimeter. Therefore, when the lengths of all sides of a triangle are doubled, the perimeter increases by a factor of two.

Thus, the answer to how many times greater