Q15
If the length of a side of a rhombus is 36 cm and the area of the rhombus is 396 sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is
Answer: 60
Key idea: The diagonals of a rhombus bisect each other at right angles, giving \(d_1^2+d_2^2=4a^2\) and area \(=\frac12d_1d_2\).
- \(d_1^2+d_2^2=4\times36^2=5184\).
- \(\frac12d_1d_2=396\Rightarrow d_1d_2=792\), so \(2d_1d_2=1584\).
- \((d_1-d_2)^2=5184-1584=3600\Rightarrow|d_1-d_2|=60\).
Hence, the answer is 60.