Question

Rectangle has a side of x+2 and 3x+2 and a triangle has sides of 5x-1 and 3(x-2) and 2x+5. If both shapes have the same perimeter, what is x?

(Next Question) Determine the perimeter of each shape.

(Final Question) Determine a simplified expression for the perimeter of each shape.

Answer 1

Step-by-step explanation:

perimeter of rectangle = 2( length + breadth) length = x+2 , breadth = 3x+2

perimeter of rectangle = 2( x+2 +3x +2 )

perimeter of rectangle= 2( 4 x +4)

perimeter of rectangle= 8x +8

perimeter of triangle = sum of all sides

perimeter of the triangle = 5x -1 +3(x-2 )+ 2x +5

perimeter = 5x -1 +3x - 6 +2x+5

perimeter = 10x - 7 + 5

perimeter of triangle = 10 x -2

final answer : given : perimeter of rectangle = perimeter of triangle

so then

8 x +8 = 10 x - 2

8 +2 = 10 x - 8 x

10 = 2x

10 /2 = x

5 = x

so x is 5 ...

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