Can a right triangle with sides 6cm, 10cm and 8cm be formed? Give reason.
Solution:
Given, the sides of a triangle are 6 cm, 10 cm and 8 cm.
We have to determine if the given sides form a right triangle.
According to the Pythagorean theorem,
The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.
(Hypotenuse)2 = (Base)2 + (Altitude)2
Let the hypotenuse be 10 cm
Let the base and perpendicular be 6 cm and 8 cm.
LHS: (Hypotenuse)2
(Hypotenuse)2 = (10)²
= 100
RHS: (Base)2 + (Altitude)2
(Base)2 + (Altitude)² = (6)² + (8)²
= 36 + 64
= 100
LHS = RHS
The given sides satisfy the conditions of a right triangle.
Therefore, the given sides form a right triangle.
✦ Try This: Can a right triangle with sides 3cm, 5cm and 4cm be formed? Give reason.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 3 Problem 94
Can a right triangle with sides 6cm, 10cm and 8cm be formed? Give reason
Summary:
A right triangle with sides 6cm, 10cm and 8cm can be formed, since it satisfies the Pythagorean theorem.
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