Triangle question:
If you know that the perimeter is 6x, then (x+3)+(2x+4)+?=6x, as perimeter is a measure of the sum of all the sides. So we already have 3x+7+?=6x, now we need to add another 3x and get rid of the 7, this can simply be written as 3x-7, which will be the expression for the missing side. We can check this -
x+3+2x+4+3x-7= 6x
Rectangle question:
We know that in rectangles, two pairs of sides are equal. So, the length opposite the 3x-3 is also 3x-3. Now, we know what perimeter is and the unique trait about the sides of a rectangle so the equation looks like this -
6x-6+2(?)=10x+6
Solve for x as follows:
6x-6+2(?)=10x+6
Step 1: Minus 6x on both sides
-6+2(?)=4x+6
Step 2: Add 6 on both sides
2(?)=4x+12
Step 3: Divide both sides by 2
?=2x+6
We can check if this is correct -
3x-3+3x-3+2x+6+2x+6=10x+6
