Which of triangle whose sides are given below are right angled?
answers:-
a) AB = 89, AC = 80, BC = 39
b) AB = 57, AC = 50, BC = 45
c) AC = 34, AB = 20, BC = 21
d) AC = 50, AB = 32, BC = 20
Answers
options can right answer or wrong answer
Given : Triangle sides
To Find : triangle whose sides are given below are right angled
a) AB = 89, AC = 80, BC = 39
b) AB = 57, AC = 50, BC = 45
c) AC = 34, AB = 20, BC = 21
d) AC = 50, AB = 32, BC = 20
Solution:
A triangle with sides a, b and c
Converse of the Pythagorean Theorem
A triangle in which the sum of the squares of the lengths of two sides is equal to the square of the length of the third side is a right triangle.
c² = a² + b² where c is the largest side of the triangle
a) AB = 89, AC = 80, BC = 39
89² = 7921
80² = 6400
39² = 1521
7921 = 6400 + 1521
Hence triangle is right angled triangle
b) AB = 57, AC = 50, BC = 45
57² = 3249
50² = 2500
45² = 2025
=> 3249 ≠ 2500 + 2025
Hence triangle is not right angle triangle
c) AC = 34, AB = 20, BC = 21
34² ≠ 20² + 21²
Hence triangle is not right angle triangle
d) AC = 50, AB = 32, BC = 20
50² ≠ 32² + 20²
Hence triangle is not right angle triangle
AB = 89, AC = 80, BC = 39 is right angled triangle
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