What will be the other diagonal of a rhombus if its perimeter is 146cm and one of the diagonal is 55cm. Also find the area of rhombus.
Answers
The perimeter of a rhombus = 4 x side
146.
146/4.
36.5.
= 4 x side
= side
= 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.
Answer
48 cm
Step-by-step explanation:
find the lenght of one side
perimeter =48cm
lenght =perimeter÷4
length =146÷4=36.5
find 1/2 of known diagonal
1/2of the diagonal =55÷2=27.5cm
find 1/2of the other diagonal
let 1/2:of the other diagonal be x
a^2 +b^2=c^2
x^2 + 27.5^2 =36.5^2
x^2=36.5^2 -27.5^2
x^2=576
x=24
find the lenght of the other diagonal
1/2the lenght =24
the lenght =24×2=48