Question
Download Solution PDFIf two diagonals of a rhombus are in the ratio 5 ∶ 12. Find the area of the rhombus if length of the side of the rhombus is 26 cm.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Two diagonals of a rhombus are in the ratio = 5 ∶ 12
Length of side = 26 cm
Concept used:
The two diagonals bisect each other at 90° in a rhombus.
Formula used:
Area of rhombus = (1/2) × Product of the two diagonals
Calculations:
Let the diagonals of rhombus be 5x and 12x
If the two diagonals of rhombus ABCD intersect at O then,
⇒ AO2 + BO2 = AB2
⇒ (5x/2)2 + (12x/2)2 = 262
⇒ (25x2/4) + (144x2/4) = 676
⇒ 169x2 = 676 × 4
⇒ 169x2 = 2704
⇒ x2 = 16
⇒ x = 4 cm
Diagonals, 5x = 20 cm and 12x = 48 cm
Area of rhombus = (1/2) × 20 × 48
⇒ 10 × 48
⇒ 480 cm2
∴ The area of the rhombus is 480 cm2
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