A rectangle having 10 cm and 6 cm as its dimensions was reconstructed to make a rhombus having the same perimeter as that of the rectangle and 60° as one of its angles. The area of the rhombus, in cm², was:

Question

Question

This question was previously asked in

RRB ALP CBT I 29 Aug 2018 Shift 1 Official Paper

Answer 1

Given:

Length of rectangle = 10 cm

Breadth of rectangle = 6 cm

Rectangle is reconstructed into Rhombus.

Perimeter of the rectangle is equal to the perimeter of rhombus.

One of the angles of the rhombus is 60°.

Concept Used:

Perimeter of Rectangle = 2(L + B)

Perimeter of Rhombus = 4(side)

Area of Rhombus = (side)2 × sin A

Calculation:

Length of rectangle, L = 10 cm

Breadth of rectangle, B = 6 cm

Perimeter of Rectangle = 2(L + B)

⇒ 2(10 + 6)

⇒ 2(16)

⇒ 32 cm

Perimeter of the rectangle = Perimeter of rhombus

⇒ 4(side) = 32

⇒ side = 32/4 = 8

Area of Rhombus = (side)2 × sin A [where A is any angle of rhombus]

⇒ Area = 82 × sin 60°

⇒ 64 × √3/2

⇒ 32√3 cm2

∴ Area of the rhombus 32√3 cm2.