The perimeter of a rhombus is 74 cm and one of its diagonals is 35 cm. What is the length of other diagonal?
Answer:
12 cm
- One way to solve this is as follows:
We know that,
a) The sides of a rhombus are equal. Therefore one side =
= 18.574 4
b) A diagonal of a rhombus divides the rhombus into 2 equal triangles.
c) The area of a rhombus is
(Diagonal1 × Diagonal2) ------(1)1 2 - Taking one of the two triangles formed by the diagonal with length 35 cm.
Area (using Heron's formula) = √S(S−18.5)(S−18.5)(S−35)
Where, S =
=2 × 18.5 + 35 2
= 3672 2
Area = √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) = 2101 2
⇒
(35 × Diagonal2) = 2101 2
⇒ Diagonal2 = 2 ×
= 12 cm210 35