Question

If the side of rhombus is 13 cm and one of its diagonals is 24 cm, then what will be length of the other diagonal?

(a) 8.4 cm

(b) 4 cm

(c) 11 cm

(d) 10 cm

The question was asked in an international level competition.

My question is based upon Pythagoras Theorem topic in section Triangles of Mathematics – Class 10

Answer 1

The correct choice is (d) 10 cm

Best explanation: ABCD is a rhombus. The side of the rhombus is 13 cm and the length of one of its diagonal is 24 cm.

Let the length of other diagonal be 2x cm.

Since, diagonals of a rhombus bisect each other. Therefore, AE = x cm and DE = 12 cm

Now, in ∆AED

AD^2 = AE^2 + DE^2

13^2 = x^2 + 12^2     (Since, AD is the altitude of the triangle it will bisect BC)

x^2 = 169 – 144

x^2 = 25

x = √25 = 5 cm

AC = 2 × AE = 2 × 5 = 10 cm