Question

Perimeter of rhombus is 146cm and length of one of
its diagonals is
55cm. Find the length of
the other diagonal and area of
the
rhombus.​

Answer 1

The perimeter of a rhombus = 4 × side

146. = 4 × side

146/4. = side

36.5. = side

Therefore side of a side of a rhombus is 36.5cm

Area of a rhombus = (side)^2

= (36.5)^2

= 1332.25

Therefore area of a rhombus is 1332.25 cm

Diagonals of rhombus are perpendicular bisector of each.

We know that one of the diagonals has length 55 cm, and therefore its half is 27.5 cm.

We also know that the length of the side is 36.5 cm.

Let the length of the other diagonal be x cm.

Hence by using Pythagoras theorem, we can conclude that

(36.5)^2 = (27.5)^2 + (x / 2)^2

Therefore (x * x) / 4 = 1332.25 - 756.25 = 576

Hence x * x = 576 * 4

Thus x = 24 * 2 = 48.

Therefore other diagonal of rhombus is 48 cm.

Hope it help you.