Pythagoras Theorem — Flashcards
Maharashtra Board · Class 10 · Mathematics
28 flashcards for Pythagoras Theorem (Maharashtra Board Class 10 Mathematics) to test yourself on key terms and facts.
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Solve: In a right angled triangle, if the two perpendicular sides are 3 cm and 4 cm, find the hypotenuse.
Answer
Step 1: Use Pythagoras theorem: AC^2 = AB^2 + BC^2. Step 2: Substitute the given lengths: hypotenuse^2 = 3^2 + 4^2. Step 3: Calculate: hypotenuse^2 = 9 + 16 = 25. Step 4: Take square root: hypotenuse …
Solve: In right angled triangle PQR, if PQ = 6 cm and QR = 8 cm, find PR.
Answer
Step 1: In triangle PQR with angle PQR = 90°, PR is the hypotenuse. Step 2: Use PR^2 = PQ^2 + QR^2. Step 3: Substitute: PR^2 = 6^2 + 8^2. Step 4: PR^2 = 36 + 64 = 100. Step 5: PR = 10 cm. Answer: PR =…
Find the missing side: A right angled triangle has hypotenuse 13 cm and one leg 5 cm. Find the other leg.
Answer
Step 1: Use hypotenuse^2 = sum of squares of the other two sides. Step 2: Let the missing leg be x. Step 3: 13^2 = 5^2 + x^2. Step 4: 169 = 25 + x^2. Step 5: x^2 = 144. Step 6: x = 12 cm. Answer: 12 c…
Check whether 11, 60, 61 is a Pythagorean triplet.
Answer
Step 1: Find the largest number: 61. Step 2: Square it: 61^2 = 3721. Step 3: Square the other two numbers: 11^2 = 121 and 60^2 = 3600. Step 4: Add the smaller squares: 121 + 3600 = 3721. Step 5: Since…
Check whether 3, 4, 5 is a Pythagorean triplet.
Answer
Step 1: Largest number = 5. Step 2: Square it: 5^2 = 25. Step 3: Square the other two numbers: 3^2 = 9 and 4^2 = 16. Step 4: Add: 9 + 16 = 25. Step 5: Since 5^2 = 3^2 + 4^2, it is a Pythagorean triple…
Use the formula [(a^2 + b^2), (a^2 - b^2), (2ab)] with a = 5 and b = 3.
Answer
Step 1: Check the condition a > b. Here, 5 > 3, so the formula can be used. Step 2: Compute a^2 + b^2 = 25 + 9 = 34. Step 3: Compute a^2 - b^2 = 25 - 9 = 16. Step 4: Compute 2ab = 2 × 5 × 3 = 30. Step…
Why must a > b in the Pythagorean triplet formula [(a^2 + b^2), (a^2 - b^2), (2ab)]?
Answer
Step 1: Look at the term a^2 - b^2. Step 2: If a > b, then a^2 > b^2, so this term stays positive. Step 3: A Pythagorean triplet uses natural numbers, so a negative number would not work. Step 4: Exam…
Find MN and LM if LN = 6 cm in a 30°-60°-90° triangle LMN.
Answer
Step 1: Use MN = (1/2) × LN. Step 2: MN = (1/2) × 6 = 3 cm. Step 3: Use LM = (√3/2) × LN. Step 4: LM = (√3/2) × 6 = 3√3 cm. Answer: MN = 3 cm and LM = 3√3 cm.
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