Question 1

Given a triangle with sides $$x$$, $$6x$$, and $$11x - 10$$, and a perimeter of 224 feet, which equation correctly represents the relationship among the sides and the perimeter?

Accepted Answer

$$x + 6x + 11x - 10 = 224$$

Question 2

What is the value of $$x$$ that satisfies the equation $$x + 6x + 11x - 10 = 224$$?

Accepted Answer

$$x = 13$$

Question 3

If $$x = 13$$, what is the length of the side represented by $$6x$$?

Accepted Answer

$$78$$ feet

Question 4

Calculate the length of the side represented by $$11x - 10$$ when $$x = 13.$$

Accepted Answer

$$133$$ feet

Question 5

What is the sum of the three sides when $$x = 13$$?

Accepted Answer

$$224$$ feet

Question 6

Which of the following steps is necessary to isolate $$x in $$the equation $$18x - 10 = 224$$?

Accepted Answer

Add $$10 to $$both sides

Question 7

After adding $$10 to $$both sides of $$18x - 10 = 224$$, what is the resulting equation?

Accepted Answer

$$18x = 234$$

Question 8

What is the final step to solve for $$x in$$ $$18x = 234$$?

Accepted Answer

Divide both sides by $$18$$

Question 9

If the perimeter of a triangle is the sum of its sides, which of the following best describes the process to check your solution?

Accepted Answer

Add the calculated side lengths and compare to the given perimeter

Question 10

Suppose the side lengths of a triangle are $$x$$, $$6x$$, and $$11x - 10. If $$the perimeter is increased by $$18$$ feet, what is the new equation to solve for $$x$$?

Accepted Answer

$$x + 6x + 11x - 10 = 242$$

Question 11

If the side lengths of a triangle are $$x$$, $$6x$$, and $$11x - 10$$, and $$x$$ must be a positive integer, which of the following is a valid value for $$x if $$the perimeter is $$224$$ feet?

Accepted Answer

$$13$$

Question 12

Which property of equality is used when adding $$10 to $$both sides of the equation $$18x - 10 = 224$$?

Accepted Answer

Addition property of equality

Question 13

If the side lengths of a triangle are $$x$$, $$6x$$, and $$11x - 10$$, and $$x = 13$$, which side is the longest?

Accepted Answer

$$11x - 10$$

Question 14

A triangle has sides $$x$$, $$6x$$, and $$11x - 10. If$$ $$x is $$doubled, what happens to the perimeter?

Accepted Answer

It nearly doubles, but is reduced by $$10$$

Solving Perimeter Problems with Linear Equations

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