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If three sides of a right-angled triangle are (k – 4) cm, k, and (k + 4), then the value of k is:

  1. 8
  2. 4
  3. 12
  4. 16

Answer (Detailed Solution Below)

Option 4 : 16
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Detailed Solution

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Given:

Three sides of the triangle are (k – 4), k and (k + 4).

Formula:

As we know,

Pythagoras Theorem

(Hypotenuse)2 = (Perpendicular)2 + (Base)2

Calculation:

According to the question

(k + 4)2 = (k – 4)2 + k2

⇒ k2 + 16 + 8k = k2 + 16 – 8k + k2

⇒ k2 = 16k

⇒ k = 16

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