A) To calculate the length of the other diagonal, we can use the formula for the area of a rhombus:
Area = (d1 * d2) / 2
where d1 and d2 are the lengths of the diagonals. We're given that the area is 96cm² and one diagonal is 12cm.
Plugging in the values:
96 = (12 * d2) / 2
192 = 12 * d2
d2 = 16
So, the other diagonal is 16cm.
B) To calculate the sides of the rhombus, we can use the formula for the area of a rhombus again:
Area = (d1 * d2) / 2
where d1 and d2 are the lengths of the diagonals, and we know that one diagonal is 12cm and the other is 16cm.
Plugging in the values:
96 = (12 * 16) / 2
96 = 192 / 2
96 = 96
This checks out, so the sides of the rhombus are equal and each side is equal to 12cm.
C) The perimeter of a rhombus is simply the sum of all four sides:
Perimeter = 4 * side
Plugging in the value for the side:
Perimeter = 4 * 12
Perimeter = 48
Therefore, the perimeter of the rhombus is 48cm.
The area and a diagonal of a rhombus are 96cm² and 12cm respectively. Calculate
A)the length of the other diagonal
B)the sides of the rhombus
C) the perimeter of the rhombus
1 answer