5. Sometimes you can do these in your head. If you add 5 feet to the shortest side, then all three are the same length and the perimeter is 39 ft. That means the two longest sides are 39/3 = 13 ft, and the short side is 13-5 = 8 ft.
side 1, 2, 3 = (8, 13, 13) ft; perimeter is given as 34 ft.
6. Let s represent the first side. Then the second side is 3s and the third side is s-9. The sum of the side lengths is
... s + 3s + (s-9) = 61
... 5s -9 = 61 . . . . . . . . . simplify
... s = (61 +9)/5 = 14 . . . add 9 to both sides; divide both sides by 5
side 1, 2, 3 = (14, 42, 5) ft; perimeter is given as 61 ft.
⇒ Once again, these side lengths <em>cannot form a triangle</em>.
7. This problem is word-for-word identical to your problem 3, so has the same answer.
side 1, 2, 3 = (9, 2, 36) ft; perimeter is given as 47 ft.
⇒ And yet again, these side lengths <em>cannot form a triangle</em>.
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The equation of problem 6 is sometimes referred to as a "two-step" linear equation. It has a constant added on the side of the equation with the variable term. You solve it by adding the opposite of that constant to both sides of the equation (first step). Doing that leaves the variable term by itself. Then you divide both sides of the equation by the coefficient of the variable (second step). That leaves the variable by itself, and gives you its value on the other side of the equal sign.
Here, we have shown the addition and division on one line: (61 +9)/5. Since you're working problems like this, we presume you know how to solve two-step equations, so this should not be anything new.
