Question

If the area of a rhombus is 864 cm² and one of its diagonals is 48 cm, find the other diagonal and perimeter.

Answer 1

Given:

• Area of the rhombus = 864 cm²
• One diagonal (d₁) = 48 cm
• Need to find the other diagonal (d₂) and the perimeter

Step wise calculation:

1. Area of a rhombus formula:

`"Area" = 1/2 xx d_1 xx d_2`

2. Substitute known values and calculate the other diagonal (d₂): 

`864 = 1/2 xx 48 xx d_2`

`864 = 24 xx d_2`

`d_2 = 864/24`

d₂ = 36 cm

3. To find the perimeter, first calculate the side length of the rhombus. 

The diagonals bisect each other at right angles, so half of each diagonal forms a right triangle with the side as hypotenuse.

Side = s

= `sqrt((d_1/2)^2 + (d_2/2)^2`

= `sqrt(24^2 + 18^2)`

`s = sqrt(576 + 324)`

= `sqrt(900)`

= 30 cm

4. Perimeter (P) of rhombus is:

P = 4 × s

= 4 × 30

= 120 cm

Thus, the other diagonal is 36 cm and the perimeter is 120 cm.