# Texas Go Math Grade 8 Lesson 13.3 Answer Key Dilations and Measurement

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## Texas Go Math Grade 8 Lesson 13.3 Answer Key Dilations and Measurement

Exploring Dilations and Measurement

The blue rectangle is a dilation (enlargement) of the green rectangle.

A. Using a centimeter ruler, measure and record the length of each side of both rectangles. Then calculate the ratios of all pairs of corresponding sides.

What is true about the ratios that you calculated?

What scale factor was used to dilate the green rectangle to the blue rectangle?

How are the side lengths of the blue rectangle related to the side lengths of the green rectangle?

B. What is the perimeter of the green rectangle? _______________
What is the perimeter of the blue rectangle? _______________
How is the perimeter of the blue rectangle related to the perimeter of the green rectangle?

C. What is the area of the green rectangle? _______________
What is the area of the blue rectangle? _______________
How is the area of the blue rectangle related to the area of the green rectangle?

Reflect

Question 1.
Make a Conjecture The perimeter and area of two shapes before and after dilation are given. How are the perimeter and area of a dilated figure related to the perimeter and area of the original figure?

Question 2.
Johnson Middle School is selling mouse pads that are replicas of a student’s award-winning artwork. The rectangular mouse pads are dilated from the original artwork and have a length of 9 inches and a width of 8 inches. The perimeter of the original artwork is 136 inches. What is the area of the original artwork?

Find the perimeter and area of the image after dilating the figures shown with the given scale factor. (Explore Activity and Example 1)

Question 1.
Scale factor = 5

Question 2.
Scale factor = $$\frac{3}{4}$$

A group of friends is roping off a soccer field in a back yard. A full-size soccer field is a rectangle with a length of 100 yards and a width of 60 yards. To fit the field in the back yard, the group needs to reduce the size of the field so its perimeter is 128 yards. (Example 1)

Question 3.
What is the perimeter of the full-size soccer field?

Question 4.
What is the scale factor of the dilation?

Question 5.
What is the area of the soccer field in the back yard?.

Essential Question Check-In

Question 6.
When a rectangle is dilated, how do the perimeter and area of the rectangle change?

Question 7.
When you make a photocopy of an image, is the photocopy a dilation? What is the scale factor? How do the perimeter and area change?

Question 8.
Problem Solving The universally accepted film size for movies has a width of 35 millimeters. If you want to project a movie onto a square sheet that has an area of 100 square meters, what is the scale factor that is needed for the projection of the movie? Explain.

Question 9.
The perimeter of a square is 48 centimeters. If the square is dilated by a scale factor of 0.75, what is the length of each side of the new square?

Question 10.
The screen of an eReader has a length of 8 inches and a width of 6 inches. Can the page content from an atlas that measures 19 inches by 12 inches be replicated in the eReader? If not, propose a solution to move the atlas content into the eReader format.

Question 11.
Represent Real-World Problems There are 64 squares on a chessboard. Each square on a tournament chessboard measures 2.25 × 2.25 inches. A travel chessboard is a dilated replica of the tournament chessboard using a scale factor of $$\frac{1}{3}$$.

a. What is the size of each square on the travel chessboard?

b. How long is each side of the travel board?

c. How much table space do you need to play on the travel chessboard?

Question 12.
Draw Conclusions The legs of a right triangle are 3 units and 4 units long. Another right triangle is dilated from this triangle using a scale factor of 3. What are the side lengths and the perimeter of the dilated triangle?

H.O.T. Focus on Higher Order Thinking

Question 13.
Critique Reasoning Rectangle W’X’Y’Z’ below is a dilation of rectangle WXYZ. A student calculated the area of rectangle W’X’Y’Z’ to be 36 square units. Do you agree with this student’s calculation? If not, explain and correct the mistake.