the perimeter of a rhombus is 146 CM one of its diagonal is 55 cm find the other diagonal and the area of the Rhombus
Answers
146. = 4 × side
146/4. = side
36.5. = side
Therefore side of a side of a rhombus is 36.5cm
Area of a rhombus = (side)^2
= (36.5)^2
= 1332.25
Therefore area of a rhombus is 1332.25 cm
Diagonals of rhombus are perpendicular bisector of each.
We know that one of the diagonals has length 55 cm, and therefore its half is 27.5 cm.
We also know that the length of the side is 36.5 cm.
Let the length of the other diagonal be x cm.
Hence by using Pythagoras theorem, we can conclude that
(36.5)^2 = (27.5)^2 + (x / 2)^2
Therefore (x * x) / 4 = 1332.25 - 756.25 = 576
Hence x * x = 576 * 4
Thus x = 24 * 2 = 48.
Therefore other diagonal of rhombus is 48 cm.
Hope it help you.
Answer:
The length of the other diagonal is 48 cm.
The area of the rhombus is 1320 cm².
Step-by-step explanation:
The perimeter of a rhombus = 146 cm
The rhombus has all four sides equal.
Therefore, each side of the rhombus = 146/4 = 36.5 cm
The length of one diagonal is 55 cm
Let us consider a rhombus ABCD.
The diagonals of the rhombus are AC, BD bisect each other and intersect at 'O'.
The diagonals of a rhombus intersect each other at 90°.
In ΔAOB, By applying Pythagoras Theorem
AB² = AO² + OB²
36.5² = 27.5² + OB² ( 55/2 = 27.5 cm as diagonals bisect each other)
OB² = 1332.5 - 756.25
OB² = 576
OB = √576
OB = 24
Thus, BD = OB + OD
BD = 24 + 24
BD = 48 cm,
Thus, the length of the other diagonal is 48 cm.
Area of right ΔABD = 1/2 X b X h
Area = 1/2 X BD x AO
Area = 1/2 x 55 x 24
Area of ΔABD = 660 cm²
Similarly, Area of ΔBCD = 660 cm²
Hence, the total area of the rhombus ABCD is 660 + 660 = 1320 cm²
Area of the rhombus = 1320 cm²
