Question

If the sum of the diagonals of a rhombus is $10$ cm and its perimeter is $4\sqrt{13}$ cm, then the lengths of is diagonals are

• A. $5,5$
• B. $6,4$
• C. $7,3$
• D. $8,2$

Answer 1

The correct option is B $6,4$

Each side $=\sqrt{13}$.
Let one of the diagonals be $x\therefore$ other is $10-x=y$
In $△AOB,{\left(\frac{x}{2}\right)}^2+\frac{(10-x{)}^2}{2^2}=13\Rightarrow x^2+(10-x{)}^2=13\times 4=52$
$\Rightarrow 2x^2-20x+100=52\Rightarrow (x-4)(x-6)=0$
$\Rightarrow x=4,6.\Rightarrow y=6,4.$