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
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.