Mr. Grayson owns a wood company that sells trees, wood materials, and specialty items created from wood. (Score for Question 1: ___ of 4 points) 1. One of Mr. Grayson’s customers, Zenani, is creating an art wall on which she will display some art in triangular frames. She wants three frames, each in the shape of a right triangle. (a) For the first frame, Zenani already has two wooden pieces that are 13 in. and 16 in. long. Zenani says that since she wants the frame to be a right triangle, there’s only one possible measurement for the last piece of wood. Is Zenani right? If so, what is that last measurement? If not, explain why not and give all possible measurements for the last wood piece. Round to the nearest tenth. (b) For the second frame, Zenani asks Mr. Grayson to double the measurements of the first triangular frame to make a new frame in the shape of a right triangle. Will Zenani’s strategy work for the second frame? Explain why or why not. (c) For the third frame, Zenani asks Mr. Grayson to add the same measurement to each of the sides of the original triangle frame to make a new frame in the shape of a right triangle. Will Zenani’s strategy work for the third frame? Explain why or why not. Answer:   (Score for Question 2: ___ of 4 points) 2. Mr. Grayson gets a request from a customer to buy a palm tree of a specific height. Mr. Grayson’s tree nursery is very large and is organized by a coordinate plane map system. He finds a palm tree that he thinks might meet the customer’s specifications. The tree is located at coordinates . He calls his assistant to come over to help him determine the height of the tree. He asks his assistant where she’s located. His assistant says she is located at . Each unit on the coordinate grid represents 1 ft. How far is Mr. Grayson’s assistant from the tree? Round to the nearest tenth. Show your work. Answer:   (Score for Question 3: ___ of 3 points) 3. Mr. Grayson orders a box that has a volume of . The box is in the shape of a cube. What is the longest stick that can fit in the box? Round your answers to the nearest whole number. Answer:  Please answer All of the questions to get the points

Accepted Solution

Question 1:
A) No; 9.3 or 20.6.
B) Yes, because the triangles are similar.
C) No, because the triangles will not necessarily be similar.

There is not enough information to answer Questions 2 or 3.

Explanation for Question 1:
A) We are not told which side is the longest, so these two sides could be placed anywhere in the Pythagorean theorem.  They could either be both legs, or one could be the hypotenuse:

Hypotenuse: 13² + b² = 16²
                     169 + b² = 256
                     169 + b² - 169 = 256 - 169
                      b² = 87
                      b = √87 = 9.3

Both legs:   13² + 16² = c²
                   169 + 256 = c²
                   425 = c²
                   √425 = c
                   20.6 = c

B) The two triangles will be similar, since each pair of corresponding sides will have the same ratio (2, since it is doubled).  Similar triangles have the same angle measures, so this must also be a right triangle.

C) Simply adding a value to each side will not preserve similarity.  For example, if we had a triangle with sides 3, 4, and 5, adding 2 to each side would give us 5, 6 and 11.  These do not have the same ratios; 3/5 is not the same as 4/6 or 5/11.