Advertisements
Advertisements
Question
If the diagonals of a rhombus are 18 cm and 24 cm respectively, then its side is equal to
Options
16 cm
15 cm
20 cm
17 cm
Advertisements
Solution
Let ABCD be rhombus with diagonals AC and BD 18cm and 24cm respectively.
We know that diagonals of the rhombus bisect each other at right angles.
Therefore,
`AO = 1/2 AC `
`AO = 1/2 (18cm) `
AO = 9cm
Similarly,
`BO = 1/2 BD `
`BO = 1/2(24cm)`
BO = 12cm
Also, ΔAOB is a right angled triangle.
By Pythagoras theorem, we get:
`AB^2 = AO^2 + BO^2`
`AB = sqrt(AO^2 + BO^2)`
`AB = sqrt(9^2 + 12^2)`
`AB = sqrt225`
AB = 15cm
Hence the correct choice is (b).
APPEARS IN
RELATED QUESTIONS
In a quadrilateral ABCD, CO and DO are the bisectors of `∠`C and ∠D respectively. Prove that
`∠`COD = `1/2` (`∠`A+ `∠`B).
Two opposite angles of a parallelogram are (3x – 2)° and (50 – x)°. Find the measure of each angle of the parallelogram .
In Fig. below, ABCD is a parallelogram in which ∠DAB = 75° and ∠DBC = 60°. Compute
∠CDB and ∠ADB.
In the given figure, PQRS is a rhombus in which the diagonal PR is produced to T. If ∠SRT = 152°, find x, y and z.
In a rhombus ABCD, if ∠ACB = 40°, then ∠ADB =
Can the angles 110º, 80º, 70º and 95º be the angles of a quadrilateral? Why or why not?
Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.
Can all the angles of a quadrilateral be right angles? Give reason for your answer.
In the following figure, P is the mid-point of side BC of a parallelogram ABCD such that ∠BAP = ∠DAP. Prove that AD = 2CD.
In a quadrilateral PQRS, ∠P = 50°, ∠Q = 50°, ∠R = 60°. Find ∠S. Is this quadrilateral convex or concave?
