In an isosceles triangle ABC, if AB = AC = 25 cm and BC = 14 cm, then the measure of altitude from A on BC is
An isosceles triangle is a triangle with two equal sides and two equal angles opposite those sides. The third side is called the base and the angle opposite the base is the vertex angle. It shows symmetry along the altitude drawn from the vertex angle to the base and is fundamental in geometry.
Class 10 Maths Chapter 6 Triangles is essential for CBSE Exam 2024-25. It explores triangle similarity and congruence along with key theorems like Pythagoras and basic proportionality. The chapter emphasizes properties of triangles and their applications in problem-solving. A strong grasp of these concepts is crucial to excel in geometry and score well in the exam as it forms the foundation for advanced mathematical topics and practical scenarios.
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In an isosceles triangle ABC, given that AB = AC = 25 cm and BC = 14 cm, we need to find the measure of the altitude from A to BC.
Let the altitude from A meet BC at point D. Since the triangle is isosceles, the altitude AD also acts as the median, dividing BC into two equal parts:
BD = DC = BC / 2 = 14 / 2 = 7 cm.
Now, consider ΔABD, which is a right triangle because AD is perpendicular to BC. Using the Pythagorean theorem:
AB² = AD² + BD²
25² = AD² + 7²
625 = AD² + 49
AD² = 625 – 49
AD² = 576
AD = √576 = 24 cm.
Thus, the measure of the altitude from A on BC is 24 cm.
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