Question : If one diagonal of a rhombus is equal to its side, then the diagonals of the rhombus are in the ratio of:
Option 1: $\sqrt{3}:\sqrt{6}$
Option 2: $\sqrt{2}:1$
Option 3: $\sqrt{2}:\sqrt{3}$
Option 4: $1:\sqrt{3}$
New: SSC CHSL tier 1 answer key 2024 out | SSC CHSL 2024 Notification PDF
Recommended: How to crack SSC CHSL | SSC CHSL exam guide
Don't Miss: Month-wise Current Affairs | Upcoming government exams
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: $1:\sqrt{3}$
Solution : Let the side of the rhombus be $a$. In a rhombus, the diagonals bisect each other at 90°. Here, PR = $a$, So, OP = $\frac{a}{2}$ Also OQ = $\frac{SQ}{2}$ Now, $\triangle$POQ is a right-angled triangle. On applying Pythagoras theorem, we get, $PQ^2=OP^2+OQ^2$ $⇒a^2=(\frac{a}{2})^2+(\frac{SQ}{2})^2$ $⇒(\frac{SQ}{2})^2=\frac{3a^2}{4}$ $⇒\frac{SQ}{2}=\frac{\sqrt3}{2}a$ $\therefore SQ=\sqrt3 a$ So, Second diagonal = $\sqrt3a$ Ratio of first and second diagonal $= \frac{a}{\sqrt{3}a} = \frac{1}{\sqrt3}=1:\sqrt3$ Hence, the correct answer is ${1}:{\sqrt3}$.
Candidates can download this e-book to give a boost to thier preparation.
Result | Eligibility | Application | Admit Card | Answer Key | Preparation Tips | Cutoff
Question : The length of each side of a rhombus is equal to the length of the side of a square whose diagonal is $40\sqrt2$ cm. If the length of the diagonals of the rhombus is in the ratio $3:4$, then its area ( in cm2) is:
Question : If ABCD is a rhombus, AC is its smallest diagonal, and $\angle$ABC = $60^{\circ}$, find the length of a side of the rhombus when AC = 6 cm.
Question : The length of the diagonals of a rhombus is 40 cm and 60 cm. What is the length of the side of the rhombus?
Question : A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surfaces will be:
Question : The area and the length of one of the diagonals of a rhombus are 84 cm2 and 7 cm respectively. Find the length of its other diagonal (in cm).
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile