### The perimeter of a rhombus is 74 cm and one of its diagonals is 35 cm. What is the length of other diagonal?

12 cm

Step by Step Explanation:
1. One way to solve this is as follows:
We know that,
a) The sides of a rhombus are equal. Therefore one side =
 74 4
= 18.5
b) A diagonal of a rhombus divides the rhombus into 2 equal triangles.
c) The area of a rhombus is
 1 2
(Diagonal1 × Diagonal2) ------(1)
2. Taking one of the two triangles formed by the diagonal with length 35 cm.
Area (using Heron's formula) = $\sqrt{ S(S-18.5)(S-18.5)(S-35) }$
Where, S =
 2 × 18.5 + 35 2
=
 72 2
= 36
Area = $\sqrt{ 36(36-18.5)(36-18.5)(36-35) }$ = 210 ------(2)  [The details of this computation are left to the student.]
3. On comparing equation (1) and (2) we get,

 1 2
(Diagonal1 × Diagonal2) = 210
⇒
 1 2
(35 × Diagonal2) = 210
⇒ Diagonal2 = 2 ×
 210 35
= 12 cm