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

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**Answer: **12 cm

**Step by Step Explanation: **- One way to solve this is as follows:

We know that,

a) The sides of a rhombus are equal. Therefore one side = = 18.5

b) A diagonal of a rhombus divides the rhombus into 2 equal triangles.

c) The area of a rhombus is (Diagonal1 × Diagonal2) ------(1) - 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 = = = 36

Area = ^@ \sqrt{ 36(36-18.5)(36-18.5)(36-35) } ^@ = 210 ------(2) **[The details of this computation are left to the student.]** - On comparing equation (1) and (2) we get,

(Diagonal1 × Diagonal2) = 210

⇒ (35 × Diagonal2) = 210

⇒ Diagonal2 = 2 × = 12 cm