Question
Download Solution PDFThe perimeter of a rhombus is 100 cm. If one of the diagonals measures 14 cm, then the area of the rhombus is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Perimeter of the rhombus = 100 cm
Diagonal, D1 = 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 D2 are the diagonals of rhombus.
Perimeter of rhombus = 4 × Length of each side
Calculation:
Let, second diagonal = 2y
Each side of the rhombus = 100/4 cm = 25 cm
Taking a triangular segment of rhombus and applying Pythagoras theorem,
⇒ 252 – 72 = 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 cm2
∴ The area of the rhombus is 336 cm2
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