Topic Details (Notes format)

How to Classify Triangles by Sides and Angles

Subject: Mathematics

Book: Maths Mastery

Triangles can be classified by sides—equilateral (all sides equal), isosceles (two equal sides), scalene (all sides different)—or by angles—acute (all angles < 90°), right (one angle = 90°), obtuse (one angle > 90°). For example, a triangle with side lengths 3, 3, 5 is isosceles, while one with angles 30°, 60°, 90° is right-angled. Such classifications underlie geometry proofs and real-world designs like roof trusses, bridging shape fundamentals with practical engineering. Identifying the triangle type sets the stage for using the right formulas or theorems to solve deeper geometric questions.

Practice Questions

A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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If two complementary angles differ by 30°, what are the angles?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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If the sum of three consecutive integers is 72, what are the integers?

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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 a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

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What is the area of an equilateral triangle with side length 10 cm?

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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If the radius of a circle is 7 cm, what is its circumference?

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If a square has a perimeter of 64 cm, what is its area?

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