Question

The perimeter of a rhombus is 104 units. If one of its diagonals is 48 units long, find the length of the other diagonal and the area of the rhombus.

A) Diagonal length: 48 units, Area: 480 sq. units
B) Diagonal length: 56 units, Area: 600 sq. units
C) Diagonal length: 60 units, Area: 720 sq. units
D) Diagonal length: 72 units, Area: 864 sq. units

Answer 1

104/4 = 26 units per side

Length of other diagonal:

2√(26² - 24²) = 2√(676 - 576) = 2√100 =

2(10) = 20 units

Area of rhombus = 4(1/2)(10)(24)

= 480 units²

None of the choices are correct.

Answer 2

The other diagonal of the rhombus is also 48 units long. The correct area of the rhombus is 576 sq. units.

Step-by-step explanation:

To find the length of the other diagonal of the rhombus, we can use the fact that diagonals of a rhombus bisect each other at right angles. Since one diagonal is 48 units long, the other diagonal will also be 48 units long. Therefore, option A) Diagonal length: 48 units is correct.

To find the area of the rhombus, we can use the formula: Area = (diagonal1 * diagonal2) / 2. Substituting in the values, we get: Area = (48 * 48) / 2 = 1152 / 2 = 576 sq. units. Therefore, none of the given options for the area are correct.