Question

The area of rohmbus is 216cm^2 and one of its diagonal measure s 24cm find the length of other diagonal and the length of each of its side and it's perimeter.

Answer 1

Answer:

ABCD is a rhombus diagonal d1 join AC and d2 join BD, d1 and d2 is a perpendicular bisector at M.

Please draw the figure by the give statement

d1=24cm

Area of rhombus =216cm^2

Area of rhombus=1/2 * d1 *d2

216cm^ 2 = 1/2 * 24 * d2

(216 * 2)/24 = d2

d2 = 18cm

MC=d1/2=24/2

MC= 12cm

MB=d2/2=18/2

MB=9cm

In triangle BCM, using Pythagoras theorem

BC^2 = MB^2 + MC^2

BC^2 = 9^2 + 12^2

BC^2 = 81 + 144

BC^2 = 225

BC = 15 cm

Therefore, all sides of rhombus is 15cm

perimeter of rhombus = 4*side

                                       =4*15

perimeter of rhombus= 60 cm