Multiple choice

What is the area of the right-angled triangle? Statement I: The perimeter of the triangle is 5 times the base. Statement II: One of the angles of the triangle is 60°. Statement III: The length of the hypotenuse is 4 cm.

  1. Only II and III

  2. All statements together are sufficient

  3. None of these

  4. I and II or III

  5. All statements together are not sufficient
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement II gives one angle as 60°, which in a right triangle means the other acute angle is 30°. Statement III gives the hypotenuse as 4 cm. In a 30-60-90 triangle, if hypotenuse = 4 cm, then shorter side = 2 cm and longer side = 2√3 cm. Area = (1/2) × 2 × 2√3 = 2√3 cm². Statement I about perimeter being 5 times the base is unnecessary.

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