Question

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A. David notices that the shape of the Ligersville toxic dump site is somewhat like a triangle. He claims that he can approximate the perimeter of the dump site without doing any extra measurements. What assumption about side AB of the dump site would David need to make in order to justify his claim?

B. Based on the assumption in part A, determine the approximate length of side AB of the dump site. Explain your reasoning in at least two sentences.

C. Determine the approximate perimeter of the Ligersville toxic dump site. Explain your reasoning.

Answer 1

Answers and Step-by-step explanations:

A. David would need to assume that side AB is the hypotenuse of the almost-right triangle that A, B, and C make. That way, he can use the Pythagorean Theorem to solve for AB.

B. AB² = 24² + 32² = 1600  ⇒  AB = √1600 = 40 yards

We can use the Pythagorean Theorem because we assume that ABC is in the form of a right triangle, with AB as the hypotenuse. Then since whenever we have a right triangle, we can use the Pythagorean Theorem to solve for an unknown side, that applies here as well.

C. The approximate perimeter is 24 + 32 + 40 = 96 yards. Using the approximation of AB from part B, we simply add up all the side lengths of this "triangle", as that is the definition of "perimeter". Thus, when we add them all together, we get a total of 96 yards.

Answer 2

Answer:

A. Assumption: length of the curve AB is equal to the hypotenuse of the triangle formed AB was a straight line.

B. 40 yards

C. 96 yards

Step-by-step explanation:

A. Assumption: length of the curve AB is equal to the hypotenuse of the triangle formed AB was a straight line.

B. AB² = 32² + 24²

AB² = 1600

AB = 40

Since we have assumed that AB is equal to the hypotenuse, we can use pythagoras theorem to find an approximate length of AB

C. Perimeter is the sum of all lengths:

32 + 24 + 40 = 96