Teach the Pythagorean Theorem to 8th Graders
Example Output
Sure, here's a word problem that incorporates the Pythagorean Theorem in a context that 8th graders might find relatable and interesting:
Word Problem:
Sarah is excited to buy a new large screen TV for her living room. She wants to make sure that the TV will fit on her TV stand, which can comfortably hold a TV with a diagonal screen measurement of up to 55 inches.
Sarah browses online and finds a TV with a width of 48 inches and a height of 28 inches. She needs to determine if the TV will fit on her stand by calculating its diagonal measurement using the Pythagorean Theorem.
Question: Will Sarah’s chosen TV with the given dimensions fit on her stand? Use the Pythagorean Theorem to find out.
Steps to Solve:
- Start by writing down the dimensions of the TV:
- Width ((a)) = 48 inches
- Height ((b)) = 28 inches
- Apply the Pythagorean Theorem, which states: [ a^2 + b^2 = c^2 ] Where:
- (a) is the width of the TV,
- (b) is the height of the TV,
- (c) is the diagonal of the TV.
- Substitute the given values into the equation: [ 48^2 + 28^2 = c^2 ]
- Calculate (48^2) and (28^2):
- (48^2 = 2304)
- (28^2 = 784)
- Add the two results together: [ 2304 + 784 = 3088 ]
- Take the square root of 3088 to find (c): [ c = \sqrt{3088} \approx 55.57 \text{ inches} ]
- Compare the calculated diagonal length to the maximum stand capacity:
- Sarah’s TV has a diagonal measurement of approximately 55.57 inches.
- Her TV stand can hold up to a 55-inch TV.
Answer: Since 55.57 inches is slightly more than the 55-inch maximum capacity of Sarah’s TV stand, the chosen TV will not fit comfortably on her stand. Sarah should look for a TV with a slightly smaller diagonal measurement.
This problem not only helps students understand how to apply the Pythagorean Theorem but also gives them a practical example of how it can be useful in everyday situations.