JIPMAT 2025 (QA) - The cost of fencing of an equilateral triangular park and a square park is the same. If the area of the triangular park is 16sqrt(3) m^2, then the length of the diagonal of the square park is : | PYQs + Solutions

JIPMAT 2025

Geometry

Polygons

Hard

The cost of fencing of an equilateral triangular park and a square park is the same. If the area of the triangular park is $16\sqrt{3}$ m $^2$ , then the length of the diagonal of the square park is :

6\sqrt{3}

8\sqrt{3}

8\sqrt{2}

6\sqrt{2}

✅ Correct Option: 4

The cost of fencing an equilateral triangular park and a square park is the same, implying the perimeter of both parts is equal.

Let

a

be the side of the equilateral triangular park and

s

be the side of the square park.

Thus,

3a = 4s \rightarrow s = \dfrac{3}{4}a

Now, area of triangular park :

\dfrac{\sqrt3}{4} a^2 = 16 \sqrt3

Hence,

a^2 = 64

a = 8

units (since side of an equilateral triangle can't be negative)

Thus,

s = \dfrac{3}{4} \times 8 = 6

units.

Now, length of diagonal

= \sqrt 2 \times s = \sqrt2 \times 6 = 6\sqrt2

units

Hence, the correct option is Option 4.

Related questions:

JIPMAT 2025

Arrange the following in descending order based on their perimeters:
A. A square with an area of 36 sq. cm. $\newline$ B. An equilateral triangle with a side of 9 cm. $\newline$ C. A rectangle with 10 cm as length and 40 sq. cm as area. $\newline$ D. A circle with radius of 4 cm.

JIPMAT 2025 (QA) PYQs

The cost of fencing of an equilateral triangular park and a square park is the same. If the area of the triangular park is 16316\sqrt{3}163​ m2^22, then the length of the diagonal of the square park is :

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The cost of fencing of an equilateral triangular park and a square park is the same. If the area of the triangular park is $16\sqrt{3}$ m $^2$ , then the length of the diagonal of the square park is :