The area and a diagonal of a rhombus are 96cm² and 12cm respectively. Calculate

Question

A)the length of the other diagonal
B)the sides of the rhombus
C) the perimeter of the rhombus

Answer 1

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.