Question

19
Basic Mathematics (MSBTE - 1 Scheme)
13.
Area of a square is the same as the area of a rhombus.
Area of rhombus is 64 m”. One diagonal of rhombus
is twice the other find the ratio of their perimeters.
Ans. V5 : 2
​

Answer 1

Answer:

Area of rhombus=64 m square

Let one diagonal be x m

And other diagonal=2x m

Then

1/2 × x × 2x =64

x^2 =64

x = √64

x = 8 m

2x = 2×8 = 16 m

By pythagoras property

AB ^2 = OA ^2 + OB ^2

AB= √4^2+8^2

AB = √16+64

AB = √80

AB =4√5 m

Then perimeter = 4 × side =4 × 4√5 = 16√5

And

Area of square= 64 m square

side = √64 = 8 m

Then perimeter = 4 × side = 4×8=32 m

Now

Ratio = Perimeter of rhombus/Perimeter of square

= 16√5/32 = √5/2 =√5:2