How would i find the perimeter and x value from a rectangle and a triangle with the same perimeter

Question

A triangle has 3 equations for each side which include 2x+3 & 2x+3 & 10x-5. The rectangle has 5x-2 for one side and 3x-0.5 for another side.

Answer 1

Since the perimeter of a triangle/rectangle is a sum of all it’s sides, then we get (2x+3)+(2x+3)+(10x-5) for the triangle. Then, the perimeter of a rectangle will be 2(5x-2)+2(3x-0.5), each side is multiplied by two because a rectangle has two pairs of equal sides. Then, since the perimeters of two shapes are equal, then we’ll need to set them equal to each other , so we can solve for the unknown, x.

2x+3+2x+3+10x-5=10x-4+6x-1

Combining like terms:

14x+1=16x-5

Subtracting one from both sides : 14x=16x-6

Subtracting 16x from the both sides: -2x=-6

Dividing by -2: x=3

So the answers is , x=3