Question

Area of rhombus is 100 cm². If one of the diagonal is twice the other, find the length of the side of rhombus.​

Answer 1

Answer:

length of side = 5√10.

Step-by-step explanation:

let the diagonals be 'x'.

one diagonal is twice the other,

.'. d1 = x and d2 = 2x.

area of rhombus = ½ x d1 x d2

.'. 100cm² = ½(x)(2x)

.'. 100cm² = ½(2x)²

.'. 100cm² = x²

.'. x² = 100

.'. x = √100

.'. x = 10

now,

d1 = x = 10cm,

d2 = 2x = 2x10 = 20cm

To find the length of side of rhombus,

length of side of rhombus = √(d1)²+(d2)²

-----------------

2

= √(10)²+(20)²÷2

= √100+400÷2

= √500÷2

= √250

= √25x10

= 5√10cm

.'. length of side of rhombus = 5√10cm.