The diagonals of a rhombus are in the ratio of 3:4, and the area is 54cm². Find the side of the rhombus
Share
The diagonals of a rhombus are in the ratio of 3:4, and the area is 54cm². Find the side of the rhombus
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
Side of rhombus is 7.5 cm
Given :-
The diagonals of a rhombus are in the ratio of 3:4, and the area is 54cm²
To Find :-
Side
Solution :-
Let the rhombus be ABCD
AC & BD are diagonals
Now,
Let
AC = 3x & BD = 4x
Now,
We know that
[tex]{\large{\boxed{\underline{\bf Area_{(Rhombus)}=\dfrac{1}{2}\times D_1\times D_2}}}}[/tex]
=> 54 = ½ × 3x × 4x
=> 54 = ½ × 12x²
=> 54 = 6x²
=> 54/6 = x²
=> 9 = x²
=> √(9) = x
=> 3 = x
Now,
AC = 3(3) = 9 cm
BD = 4(3) = 12 cm
Let the intersecting point of the diagonals be O
We know that diagonal of rhombus bisect each other at right angles. So,
In ∆AOB
=> AO = AC/2 = 9/2 = 4.5 cm
=> OB = BD/2 = 12/2 = 6 cm
Now,
=> (AB)² = (AO)² + (OB)² [Pythagoras theorem]
=> (AB)² = (4.5)² + (6)²
=> (AB)² = 20.25 + 36
=> (AB)² = 56.25
=> AB = √(56.25)
=> AB = 7.5 cm
Therefore,
Side of square is 7.5