the two diagonals of a rhombus are length of 12cm and 16cm. calculate the length of each side of the rhombus
Answers
Answer:
Length of the side is the rhombus=√{(d1/2)^2+(d2/2)^2}. = √{(12/2)^2+(16/2)^2}. = 10 cm. Answer.
Please refer attachment for pictorial representation.
The length of the diagonals of the rhombus are 12 cm and 16 cm. As the diagonals bisect each other, we can equal measures to each part.
We also know that the diagonals of a rhombus are perpendicular bisectors meaning that that the angle at O is 90°.
Now, we can take the right angled triangle COD,
CO [Altitude] = 8 cm
OD [Base] = 6 cm
CD [Hypotenuse] = ?
As the triangle formed is right angled, we can apply the Pythagoras theorem:
Altitude² + Base² = Hypotenuse²
8² + 6² = Hypotenuse²
64 + 36 = Hypotenuse²
Hypotenuse² = 100
Hypotenuse = √100
Hypotenuse = 10 cm
Hence the measure of one side of a rhombus is 10 cm.
Knowledge Bytes:
→ Properties of Rhombus:
✳ All sides of a rhombus are equal.
✳ Opposite angles of a rhombus are equal.
✳ Adjacent angles of a rhombus add upto 180°.
✳ Opposite sides of rhombus are equal and parallel.
✳ The diagonals of a rhombus are perpendicular bisectors.
→ Area of a Rhombus
✳ 1/2 x d1 x d2
[Where d1 and d2 are two diagonals]
✳ bh
[Where b is the base and h is the height]
