Answer:
write the expression for the perimeter of the 1st rectangle 6x
write the expression for the perimeter of the 2nd rectangle 4x + 30
write the equation 6x = 4x + 30
x= 15
perimeter = 90
Step-by-step explanation:
The perimeter is adding up all the sides of the rectangle.
So for the first one, we know two of the sides: x and 2x. The opposite sides have the same values. So the other two sides are x and 2x.
Therefore, the perimeter is
2x + x + 2x + x
or
6x
Similarly with the second rectangles:
(x+12) + (x+3) + (x+12) + (x+3)
Combine like terms
x + x + x + x + 12 + 3 + 12 + 3
4x + 30
Set these two equal to each other because the two perimeters are equal
6x = 4x + 30
Subtract 4x on both sides
2x = 30
Divide by 2 on both sides
x = 15
Check:
6(15) = 4(15) + 30
90 = 60 + 30
90 = 90
The common perimeter is
6*15 = 90 units
