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

What is the sum of the interior angles of a hexagon?

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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What is the sum of the first 20 odd numbers?

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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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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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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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If x^2 - 6x + 9 = 0, what is the value of x?

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If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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