Multiple choice

If in a right-angled triangle, the hypotenuse is to be 1 cm longer than the base and 2 cm longer than the altitude, then the perimeter of the triangle will be

  1. 24 cm

  2. 20 cm

  3. 12 cm

  4. 10 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let hypotenuse be h, base b, altitude a. h = b+1, h = a+2. So b = h-1, a = h-2. By Pythagoras: (h-1)^2 + (h-2)^2 = h^2. h^2 - 2h + 1 + h^2 - 4h + 4 = h^2. h^2 - 6h + 5 = 0. (h-5)(h-1) = 0. h=5 (h=1 is impossible). Sides are 5, 4, 3. Perimeter = 5+4+3 = 12.

AI explanation

Let the hypotenuse be h, making the base h minus 1 and the altitude h minus 2. Applying the Pythagorean theorem, we get (h minus 1) squared plus (h minus 2) squared equals h squared. Expanding this gives h squared minus 6h plus 5 equals 0, so the hypotenuse is 5 cm, the base is 4 cm, and the altitude is 3 cm. The perimeter is 5 plus 4 plus 3, equaling 12 cm.

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