The diagonals of a rhombus are in the ratio 5 : 12 and its area is 240 cm². Find the lengths (in cm) of the diagonals.
10\(\sqrt2\) and 24\(\sqrt2\)
Let the diagonals be 5k and 12k. Area of a rhombus: \(\dfrac12\times d_1\times d_2 = \dfrac12\times5k\times12k = 30k^2\).
Setting this equal to 240: \(30k^2=240 \Rightarrow k^2=8 \Rightarrow k=2\sqrt2\).
Diagonals: \(5k=10\sqrt2\) cm and \(12k=24\sqrt2\) cm.
Hence, the diagonals measure \(10\sqrt2\) cm and \(24\sqrt2\) cm.
Similar Questions
- If one angle of a parallelogram is $18^\circ$ less than twice the smallest angle of the same parallelogram, then the largest angle of the parallelogram is:
- Find the area of a trapezium whose parallel sides are 10 cm and 20 cm and non-parallel sides are equal to 10 cm.
- The angles of a quadrilateral are in the ratios 2 : 4 : 6 : 8. The smallest of these angles is:
- The angles of a quadrilateral are in the ratio of 1 : 3 : 4 : 7. What is the difference between the largest and the smallest angle?
- If ABCD is a cyclic quadrilateral and ABC is an equilateral triangle find the angle of CDA.
- If one angle of a parallelogram is $39^\circ$ less than twice the smallest angle, then the smallest angle of the parallelogram is:
- If one angle of a parallelogram is $30^\circ$ less than twice the measure of the smallest angle, then the measure of the largest angle of the parallelogram is:
- In a rhombus ABCD, if $\angle ACB = 40^\circ, \text{then } \angle ADB = ?$
- P is the mid-point of side BC of a parallelogram ABCD such that $\angle BAP = \angle DAP$.
If AD = 10 cm, then CD = ? - If the angles of a quadrilateral are in the ratio of 4 : 9 : 11 : 12, then the largest of these angles is:
Important Questions from Quadrilaterals
What is the value of AC 2– BD 2
What is the point of intersection of the diagonals?
What is the area of the parallelogram?
ABCD is a cyclic quadrilateral. Diagonals BD and AC intersect each other at E. If ∠BEC = 138° and ∠ECD = 35°, then what is the measure of ∠BAC?
A circle is inscribed in a quadrilateral ABCD, touching sides AB, BC CD and DA at P, Q, R and S, respectively. If AS = 6 cm, BC = 12 cm, and CR = 5 cm, then the length of AB (in cm) is:
