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
Once you have the points they make a 3-4-5 triangle. The two legs are 3 and 4, so the hypotenuse has to be 5. Or you could use the pythagorean theorem a² + b² = c² 3² + 4² = c² 25 = c² c = 5 then find area A=1/2bh 1/2(3*4) 6
