Question

The perimeter of a rhombus is 146 cm. One of its diagonals is 55 cm. Find the length
of the other diagonal and the area of the rhombus.​

Answer 1

Answer:

Perimeter of rhombus=146cm

4×side of rhombus=146

Side of Rhombus=146÷4

Side of Rhombus=36.5 cm

The diagonal of Rhombus is 55cm

Let the other diagonal be 2x hence it's half will be x

By Pythagoras theorem

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

x^2=(36.5)^2-(27.5)^2

compare with a^2-b^2=(a+b)(a-b)

x^2=64×9

x=8×3

x=24

Hence the other diagonal is 2x =2×24=48cm

Area of rhombus=1/2×d1×d2

=1/2×55×48

=1320cm^2