Question

Find the value of X so that the rectangle and the triangle have the same perimeter. What is the perimeter?

Answer 1

The perimeter of the rectangle:

`P_r=2(x+2)+2(x+1)`
Use the distributive property: a(b + c) = ab + ac

`P_r=(2)(x)+(2)(2)+(2)(x)+(2)(1)=2x+4+2x+2=4x+6`

The perimeter of the triangle:

`P_t=(x+7)+(x+9)+(x+3)=3x+19`


`P_r=P_t\\\\4x+6=3x+19\ \ \ |-6\\4x=3x+13\ \ \ \ |-3x\\\boxed{x=13}`
substitute:

`3x+19\to (3)(13)+19=39+19=58`
Answer: 58 units.

Answer 2

Perimeter is the sum of all sides of a two-dimensional shape. Therefore, we can construct the following equation to find the value of X:

2x + 4 + 2x + 2 = x + 7 + x + 3 + x + 9
4x + 6 = 3x + 19
4x - 3x = 19 - 6
x = 13

If the perimeter of these shapes is the same, whatever which of them we use for calculating we will find the same result.

Rectangle:
13 + 2 + 13 + 2 + 13 + 1 + 13 + 1 = 58

Or

Triangle:
13 + 7 + 13 + 3 + 13 + 9 = 58

The perimeter is 58.