The base of a triangle is increased by 30 By what percentage correct to two decimal places can its h...........

Quantitative Aptitude (MTS) Percentage

The base of a triangle is increased by 30%. By what percentage (correct to two decimal places) can its height be increased so

that the area increases by 50%?

This questions was previously asked in

SSC MTS 20th October 2021 Shift-3

10.53%

12.38%

13.53%

15.38%

- Let original base = b, original height = h.

- Original area of triangle = 0.5 × b × h

- New base = b + 30% of b = 1.3b

- Let new height = xh

- Required area = Area increases by 50% ? 1.5 × (0.5 × b × h) = 0.5 × 1.3b × xh

- Set up the equation: 1.5 × 0.5 × b × h = 0.5 × 1.3b × xh

- 1.5 = 1.3x ? x = 1.5/1.3 ˜ 1.1538

- So, % increase in height = (1.1538 - 1) × 100 ˜ 15.38%

- Option 4: 15.38% is correct

- Other options are lower and can't give the required area increase with given base increase.

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