Determine whether the triangle having sides (a – 1) cm,2√a cm and (a + 1) cm is a right angled triangle.
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ABC is a right-angled triangle at B. CA is the hypotenuse.
Step-by-step explanation:
Let ABC be the triangle.
AB = a-1 cm
BC = 2√a cm
CA = (a + 1) cm
AB² = (a-1)² = a² + 1 - 2a
BC² = (2√a)² = 4a
CA = (a+1)√a = a² + 1 + 2a
AB² + BC² = a² + 1 - 2a + 4a
AB² + BC² = a² + 1 + 2a
AB² + BC² = CA²
So ABC is a right-angled triangle at B. CA is the hypotenuse.
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