The perimeter of a rhombus is 100 cm. If one of the diagonals measures 14 cm, then the area of the rhombus is:

  1. 48 cm2
  2. 96 cm2
  3. 336 cm2
  4. 672 cm2

Answer (Detailed Solution Below)

Option 3 : 336 cm2
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SSC CHSL Exam 2023 Tier-I Official Paper (Held On: 02 Aug 2023 Shift 1)
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Detailed Solution

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Given:

Perimeter of the rhombus = 100 cm

Diagonal, D= 14 cm

Concept used:

All sides of a rhombus are equal.

In a  rhombus, diagonals bisect each other perpendicularly.

Pythagoras' Theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Formula: 

Area of a rhombus = ½ × D1  × D2

Where, D1 and Dare the diagonals of rhombus.

Perimeter of rhombus = 4 × Length of each side   

Calculation:

Let, second diagonal = 2y

FT-21 2 Hindi Images Q4

Each side of the rhombus = 100/4 cm = 25 cm

Taking a triangular segment of rhombus and applying Pythagoras theorem,

⇒ 25– 7= y2

⇒ y2 = 625 – 49

⇒ y = 24 cm

So, Length of second diagonal = 2 × 24 = 48 cm

Area of the rhombus

⇒ ½ × 14 × 48 cm2

⇒ 336 cm

∴ The area of the rhombus is 336 cm2

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