Question

The side of a rhombus is 10 cm. The smaller diagonal is $\frac{1}{3}$ of the greater diagonal. Find the length of the greater diagonal :

• A. $6\sqrt{10}cm$
• B. $10\sqrt{6}cm$
• C. $6\sqrt{5}cm$
• D. $5\sqrt{6}cm$

Answer 1

The correct option is A $6\sqrt{10}cm$

Let $x$ be the length of the greater diagonal.

Then length of smaller diagonal $=\frac{x}{3}$

If we draw the two diagonals, they intersect each other and form a right angle triangle with hypotenuse as the side of rhombus, height is half of the greater diagonal and base will be half of the smaller diagonal.

$\therefore$ ${10}^2={\left(\frac{x}{2}\right)}^2+{\left(\frac{x}{6}\right)}^2$

$⟹\frac{x^2}{4}+\frac{x^2}{36}=100$

$⟹40x^2=100\times 36\times 4$

$⟹x^2=360$

$⟹x=6\sqrt{10}$ cm

Hence, option A is correct.