.
4. Which of the following can be the sides of a right
triangle?
(1) 2.5 cm.6.5 cm, 6 cm.
(ii) 2 cm. 2 cm. 5 cm.
(ii) 1.5 cm, 2cm, 2.5 cm.
In the case of right-angled triangles, identify the
right angles.
Answers
(i) 2.5 cm, 6.5 cm and 6 cm
Given three sides of a triangle are 2.5 cm, 6.5 cm and 6 cm.
Hypotenuse is known as the Largest side and from above sides, 6.5 is the larger one. So, hypotenuse is 6.5 cm.
Now, using Pythagorean theorem
H² = P² + B²
(H = Hypotenuse, P = Perpendicular, B = Base)
Substitute value of H = 6.5, P = 2.5 and B = 6
(6.5)² = (2.5)² + (6)²
42.25 = 6.25 + 36
42.25 = 42.25
L.H.S. = R.H.S.
Therefore, 2.5 cm, 6.5 cm and 6 cm are the sides of a right angled triangle.
(ii) 2 cm, 2 cm and 5 cm
Using, Pythagorean theorem
H² = P² + B²
Substitute value of H = 5, P = 2 and B = 2
(5)² = (2)² + (2)²
25 = 4 + 4
25 = 8
L.H.S. ≠ R.H.S.
Therefore, 2 cm, 2 cm and 5 cm are not the sides or don't form right angled triangle.
(iii) 1.5 cm, 2cm and 2.5 cm
Using, Pythagorean theorem
H² = P² + B²
Substitute value of H = 2.5, P = 1.5 and B = 2
(2.5)² = (1.5)² + (2)²
6.25 = 2.25 + 4
6.25 = 6.25
L.H.S. = R.H.S.
Therefore, 1.5 cm, 2cm and 2.5 cm are the sides of a right angled triangle.
Case (i) and (iii) form the right angled triangle.
Let us assume that they are forming a right angled triangle ABC where Hypotenuse is AC, Base is BC and perpendicular is AB.
So, they are forming the right angle at ∠B.