Mathematics
Grade 10
15 min
Perimeters of similar figures
Perimeters of similar figures
What you'll learn
- Identify the numbers in a word problem that need to be estimated to find the quotient with 80% accuracy.
- Solve word problems by estimating the quotient using compatible numbers, showing their work, and getting the correct answer in at least 4 out of 5 problems.
- Explain in their own words, with 100% accuracy, why estimating quotients is useful for solving real-world problems.
- Apply estimation strategies to determine if a calculated quotient in a word problem is reasonable, justifying their reasoning in writing, with 90% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define similarity and identify the similarity ratio (scale factor) between two similar figures.
State the relationship between the similarity ratio and the ratio of the perimeters of similar figures.
Calculate the perimeter of a figure given the perimeter and side lengths of a similar figure.
Determine a missing side length of a figure using the ratio of perimeters of two similar figures.
Set up and solve proportions to solve problems involving perimeters of similar figures.
Apply the concept of perimeter ratios to solve real-world application problems.
Ever wondered how architects create a tiny blueprint that perfectly represents a massive skyscraper? 🏙️ It's all about scaling, and the math behind it is simpler than you think!
This tutorial explore...
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Key Concepts & Vocabulary
TermDefinitionExample
Similar FiguresTwo geometric figures that have the exact same shape, but may have different sizes. Their corresponding angles are congruent (equal), and the ratios of their corresponding side lengths are equal.A 3 cm x 4 cm rectangle is similar to a 6 cm x 8 cm rectangle. All angles are 90°, and the ratio of corresponding sides is 6/3 = 8/4 = 2.
Corresponding SidesSides that are in the same relative position in two similar figures.In ΔABC ~ ΔXYZ, side AB corresponds to side XY, BC corresponds to YZ, and AC corresponds to XZ.
PerimeterThe total distance around the boundary of a two-dimensional shape, found by adding the lengths of all its sides.The perimeter of a triangle with side lengths 5 cm, 6 cm, and 7 cm is 5 + 6 + 7 = 18 cm.
Similarity Ratio (or Scale Factor)Th...
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Core Formulas
Similarity Ratio Formula
k = \frac{\text{side length of Figure 2}}{\text{corresponding side length of Figure 1}} = \frac{a'}{a}
Use this formula to find the scale factor (k) between two similar figures. Ensure you are consistent with which figure is the 'new' (numerator) and which is the 'original' (denominator).
Ratio of Perimeters Theorem
\frac{\text{Perimeter of Figure 2}}{\text{Perimeter of Figure 1}} = \frac{\text{side length of Figure 2}}{\text{corresponding side length of Figure 1}} \quad \text{or} \quad \frac{P'}{P} = \frac{a'}{a} = k
This is the core rule. It states that the ratio of the perimeters of two similar figures is equal to their similarity ratio. If you know the scale factor, you know the perimeter ratio, and vice-versa....
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Challenging
Right triangle ΔRST is similar to right triangle ΔUVW. In ΔRST, the legs RS and ST are 9 cm and 12 cm, respectively. The perimeter of ΔUVW is 90 cm. What is the length of the hypotenuse of ΔUVW?
A.15 cm
B.30 cm
C.37.5 cm
D.45 cm
Challenging
An architect's blueprint for a rectangular room has a scale of 1:50. The perimeter of the room on the blueprint is 72 cm. What is the actual perimeter of the room in meters?
A.1.44 meters
B.36 meters
C.14.4 meters
D.3600 meters
Challenging
Two similar polygons lie on a coordinate plane. The perimeter of Polygon A is 40 units. The perimeter of Polygon B is 50 units. The difference in length between a side on Polygon B and its corresponding side on Polygon A is 3 units. What are the lengths of these two corresponding sides?
A.Side A = 9, Side B = 12
B.Side A = 12, Side B = 15
C.Side A = 15, Side B = 18
D.Side A = 10, Side B = 13
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Frequently asked questions
What grade level is "Perimeters of similar figures"?
Perimeters of similar figures is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Perimeters of similar figures?
You'll be able to: Identify the numbers in a word problem that need to be estimated to find the quotient with 80% accuracy; Solve word problems by estimating the quotient using compatible numbers, showing their work, and getting the correct answer….
Is "Perimeters of similar figures" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Perimeters of similar figures?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.