Question

The lengths of diagonals of a rhombus are 10 cm and 8 cm. What will be the length of the sides of rhombus?

(a) 6.40 cm

(b) 5.25 cm

(c) 2.44 cm

(d) 3.29 cm

This question was addressed to me during an interview.

The query is from Pythagoras Theorem in chapter Triangles of Mathematics – Class 10

Answer 1

Right answer is (a) 6.40 cm

To elaborate: ABCD is a rhombus. The length of diagonal is 10 cm and the length of other diagonal is 8 cm.

Since, diagonals of a rhombus bisect each other. Therefore, AE = 4cm and DE = 5 cm

Now, in ∆AED

AD^2 = AE^2 + DE^2

AD^2 = 4^2 + 5 ^2     (Since, AD is the altitude of the triangle it will bisect BC)

AD^2 = 16 + 25

AD^2 = 41

AD = √41 cm = 6.40 cm