Question:hard

Gopi constructed a right-angled triangle. By modifying the dimensions of first triangle, he drew another triangle. The modifications are, the largest side is increased by 5 cm, the smallest side is doubled and the third side is increased by 50%. If the triangle formed with these new dimensions has equal angles, then what is the perimeter of the new triangle?

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Equal angles means the new triangle is equilateral, so all three new sides must be equal.
Updated On: Jul 21, 2026
  • 45 cm
  • 60 cm
  • 90 cm
  • 120 cm
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The Correct Option is C

Solution and Explanation

Step 1: Recognise the shortcut.
A right triangle whose sides scale up to become equal must start out as a scaled 3-4-5 triangle, since 3-4-5 is the simplest whole number right triangle.

Step 2: Try the multiple of 5.
Test $ a = 15 $, $ b = 20 $, $ c = 25 $ (that is, $ 3 \times 5, 4 \times 5, 5 \times 5 $). Check: $ 15^2 + 20^2 = 225 + 400 = 625 = 25^2 $, so this is a valid right triangle.

Step 3: Apply the three modifications.
Smallest side doubled: $ 2 \times 15 = 30 $.
Third side increased by 50%: $ 1.5 \times 20 = 30 $.
Largest side increased by 5: $ 25 + 5 = 30 $.

Step 4: Confirm equal angles.
All three new sides equal 30 cm, so the new triangle is equilateral and every angle is 60 degrees, matching the condition of equal angles.
This also confirms $ a = 15, b = 20, c = 25 $ is the only set of values that works, since the direct algebraic solve of $ 2a = 1.5b = c+5 $ together with $ a^2+b^2=c^2 $ gives the same unique triangle.

Final Answer:
Perimeter of the new equilateral triangle $ = 30 + 30 + 30 = 90 $ cm. $ 90 \text{ cm} $
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