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Two sides of a right triangle 5√/2 inches long. What is the perimeter of the triangle. Draw a model.

Two sides of a right triangle 5√/2 inches long. What is the perimeter of the triangle. Draw a model.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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### Problem Statement: **Topic: Geometry - Right Triangle Perimeter** **Question:** Two sides of a right triangle are 5√2 inches long. What is the perimeter of the triangle? Draw a model. ### Explanation: In this problem, you are given a right triangle with two sides measuring 5√2 inches each. This means that the triangle is an isosceles right triangle, where the two legs (the sides forming the right angle) are equal in length. The goal is to find the perimeter of the triangle and provide a model of it. #### Steps to Solve: 1. **Identify the Sides:** - Let the lengths of the legs be \( a = 5\sqrt{2} \) inches each. 2. **Calculate the Hypotenuse:** - Use the Pythagorean theorem \( a^2 + b^2 = c^2 \) to find the length of the hypotenuse. - Substitute \( a \) and \( b \) with \( 5\sqrt{2} \): \((5\sqrt{2})^2 + (5\sqrt{2})^2 = c^2\) - Simplify: \( 2 \cdot 25 = c^2 \) - Solve for \( c \): \( c = \sqrt{50} = 5\sqrt{2} \) 3. **Find the Perimeter:** - The perimeter \( P \) of the triangle is the sum of the lengths of all three sides: - \( P = a + b + c\) - Substitute the values: \( P = 5\sqrt{2} + 5\sqrt{2} + 5\sqrt{2} \) - Combine like terms: \( P = 15\sqrt{2} \) 4. **Draw the Model:** - Draw a right triangle with two equal legs each measuring \( 5\sqrt{2} \) inches and the hypotenuse also measuring \( 5\sqrt{2} \) inches. ### Conclusion: The perimeter of the right triangle is \( 15\sqrt{2} \) inches. *Note: To visualize, you can draw a right triangle where each leg is marked as \( 5\sqrt{2} \) inches and label the hypotenuse with the same length as well.*
Transcribed Image Text:### Problem Statement: **Topic: Geometry - Right Triangle Perimeter** **Question:** Two sides of a right triangle are 5√2 inches long. What is the perimeter of the triangle? Draw a model. ### Explanation: In this problem, you are given a right triangle with two sides measuring 5√2 inches each. This means that the triangle is an isosceles right triangle, where the two legs (the sides forming the right angle) are equal in length. The goal is to find the perimeter of the triangle and provide a model of it. #### Steps to Solve: 1. **Identify the Sides:** - Let the lengths of the legs be \( a = 5\sqrt{2} \) inches each. 2. **Calculate the Hypotenuse:** - Use the Pythagorean theorem \( a^2 + b^2 = c^2 \) to find the length of the hypotenuse. - Substitute \( a \) and \( b \) with \( 5\sqrt{2} \): \((5\sqrt{2})^2 + (5\sqrt{2})^2 = c^2\) - Simplify: \( 2 \cdot 25 = c^2 \) - Solve for \( c \): \( c = \sqrt{50} = 5\sqrt{2} \) 3. **Find the Perimeter:** - The perimeter \( P \) of the triangle is the sum of the lengths of all three sides: - \( P = a + b + c\) - Substitute the values: \( P = 5\sqrt{2} + 5\sqrt{2} + 5\sqrt{2} \) - Combine like terms: \( P = 15\sqrt{2} \) 4. **Draw the Model:** - Draw a right triangle with two equal legs each measuring \( 5\sqrt{2} \) inches and the hypotenuse also measuring \( 5\sqrt{2} \) inches. ### Conclusion: The perimeter of the right triangle is \( 15\sqrt{2} \) inches. *Note: To visualize, you can draw a right triangle where each leg is marked as \( 5\sqrt{2} \) inches and label the hypotenuse with the same length as well.*
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