Question

The area of a rhombus is 480 $c{m}^2$, and one of its diagonals measures 48 cm. Find (i) the length of the other diagonal, (ii) the length of each of its sides, and (iii) its perimeter.

Answer 1

Area Of Rhomus = 1/2*d1*d2

Here d1 = 48 cm

1/2*48*d2 = 480

24d2 = 480

d2 = 480/24 = 20cm

ii) Diagonals Of A Rhombus Intersect Each Other At Right Angles And Bisect Each Other.

So In Rhombus ABCD

AC = BD

Let The Mid Point Of Intersection Be O.

AO = CO

And BO = DO

AO = 1/2*48 = 24

BO = 1/2*20 = 10

Now They Form A Right Triangle

Side^2 = 24^2+10^2

Side^2 = 576+100 = 676

Side = 26 cm

iii)Perimeter Of Rhombus = 4*26 = 104cm