Topic Details (Notes format)

How to Use the Pythagorean Theorem

Subject: Mathematics

Book: Maths Mastery

The Pythagorean Theorem, a² + b² = c², applies to right-angled triangles, where c represents the hypotenuse (longest side) and a, b are the legs. For instance, if a = 3 cm and b = 4 cm, c = √(3² + 4²) = √25 = 5 cm. This theorem underlies trigonometry, enabling distance calculations in navigation, construction, and design. From verifying corners in building layouts to analyzing diagonal distances on a computer screen, Pythagoras’s principle is indispensable in geometry and everyday spatial reasoning.

Practice Questions

A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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What is the value of x if 3x + 7 = 16?

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The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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If x - y = 5 and x + y = 15, what is the value of x?

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If the length of a rectangle is doubled and the width is halved, what is the change in area?

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A train 150 m long passes a pole in 15 seconds. What is its speed?

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