Question

The adjacent sides of a parallelogram are $15cmand10cm$. If length of one diagonal of this parallelogram is $20cm$, the length of other diagonal will be

• A. $30cm$
• B. $5\sqrt{10}cm$
• C. $10\sqrt{5}cm$
• D. $4\sqrt{30}cm$

Answer 1

Answer: (B)

$5\sqrt{10}cm$

In a parallelogram, the relationship between the diagonals and the sides is ${d_1}^2+{d_2}^2=2(a^2+b^2)$ where $d_{1}and{d}_2$ are the diagonal lengths and 'a' and 'b' are the sides of the parallelogram.
So, ${d_1}^2+{d_2}^2=2(a^2+b^2)⟹{d_1}^2+{20}^2=2({10}^2+{15}^2)⟹{d_1}^2+400=2(100+225)⟹{d_1}^2=650-400=250⟹d_1=\sqrt{250}=\sqrt{25\ast 10}⟹d_1=5\sqrt{10}$
The length of the other diagonal is $5\sqrt{10}$ cm.