Find the perimeter of a rhombus whose one diagonal is 16 cm long and the area is 240 cm².

Question

Accepted Answer

The area of a rhombus is given by:  
$$
	ext{Area} = \frac{1}{2} 	imes d_1 	imes d_2
$$  
where $$ d_1 $$ and $$ d_2 $$ are the lengths of the diagonals.

Given:  
- Area = 240 cm²  
- $$ d_1 = 16 \, 	ext{cm} $$

Substitute into the formula to find $$ d_2 $$:  
$$
240 = \frac{1}{2} 	imes 16 	imes d_2
$$  
$$
d_2 = \frac{240 	imes 2}{16} = 30 \, 	ext{cm}.
$$

The perimeter of a rhombus is calculated using the formula:  
$$
	ext{Perimeter} = 2 \sqrt{(d_1/2)^2 + (d_2/2)^2}.
$$

Substitute $$ d_1 = 16 \, 	ext{cm} $$ and $$ d_2 = 30 \, 	ext{cm} $$:  
$$
	ext{Perimeter} = 2 \sqrt{\left(\frac{16}{2}ight)^2 + \left(\frac{30}{2}ight)^2}
$$  
$$
= 2 \sqrt{8^2 + 15^2}
$$  
$$
= 2 \sqrt{64 + 225}
$$  
$$
= 2 \sqrt{289}
$$  
$$
= 2 	imes 17 = 68 \, 	ext{cm}.
$$

Thus, the perimeter of the rhombus is **68 cm**.

Answer

Answer

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