The area of a triangular field with sides 60 m 175 m and 185 m is equal to that of a rectangular par...........

Quantitative Aptitude (MTS) Mensuration 2D

The area of a triangular field with sides 60 m, 175 m and 185 m is equal to that of a rectangular park whose sides are in the

ratio of 21 : 10. The perimeter (in m) of the park is:

This questions was previously asked in

SSC MTS 26th October 2021 Shift-2

341

403

372

310

Here’s how you break it down:

- We’re given a triangle with sides 60 m, 175 m, and 185 m. To find its area, Heron's formula does the trick:

- s = (60+175+185)/2 = 210

- Area = v[210×(210-60)×(210-175)×(210-185)] = v[210×150×35×25] = v(27,562,500) = 5250 m²

- The rectangular park has the same area: 5250 m². The sides are in a 21:10 ratio.

- Let the sides be 21x and 10x, so 21x × 10x = 210x² = 5250

- x² = 5250 / 210 = 25, so x = 5

- The actual sides: 21x = 105 m and 10x = 50 m

- Perimeter = 2 × (105 + 50) = 2 × 155 = 310 m

Now, about those options:

1. 341 (not it)

2. 403 (nope)

3. 372 (close, but not quite)

4. 310 (this nails it)

So, option 4 is absolutely right.

310 m is the correct perimeter.

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