Question

The area of a rhombus is 24cm² and one of its diagonals is 6 cm, then its sides is________

Answer 1

Step-by-step explanation:

Area of rhombus = 1/2 * d1 * d2

Area of Rhombus = 1/2 * 6 * d2

Area of Rhombus = 3 * d2

24/3 = d2

Diagonal ( d2 ) = 8cm

By using Pythagoras Theorem,

1/2 * ( d1 )² + 1/2 * ( d2 )² = Side²

1/2 * 6² + 1/2 * 8² = Side²

1/2 * 36 + 1/2 * 64 = Side²

13 + 32 = Side²

45 = Side²

Side = √45 cm

Answer 2

GiveN :-

• Area of rhombus = 24 cm²

• Diagonal of rhombus ( d1 ) = 6 cm

To FinD :-

• Other diagonal ( d2 ) of the rhombus

SolutioN :-

$\longrightarrow \boxed{ \bf Area_{rhombus} = \frac{d_1 \times d_2}{2}} \\ \\\longrightarrow \sf 24 = \frac{6 \times d_2}{2} \\ \\\longrightarrow \sf d_2 = \frac{24}{3} \\ \\ \longrightarrow \boxed{ \sf d_2 = 8 \: cm}$

Let a be the side of rhombus and 4 and 3 are perpendicular and base of triangle

$\longrightarrow \sf {a}^{2} = {p}^{2} + {b}^{2} \\ \\ \longrightarrow \sf {a}^{2} = {4}^{2} + {3}^{2} \\ \\ \longrightarrow \sf {a}^{2} = 16 + 9 \\ \\ \longrightarrow \sf {a}^{2} = 25 \\ \\\longrightarrow \sf a = \sqrt{25} \\ \\\longrightarrow \sf a = 5 \: cm$

Side of the rhombus is 5 cm