Question

the diagonals of rhombus are 15 cm and 20 cm what is its
perimeter

Answer 1

Answer:

50 cm

Step-by-step explanation:

The sides of a rhombus are all congruent. (the same length).

⇒  AB = BC = CD = DA

The two diagonals are perpendicular, and they bisect each other. This means they cut each other in half.

AO = OC = 1/2 * AC; BO = OD = 1/2 * BD.

Given, Diagonals are 15 cm and 20 cm.

AO = 15/2 = 7.5 cm

BO = BD/2 = 20/2 = 10 cm.

From Pythagoras theorem, we know that

AB² = AO² + OB²

     = (7.5)² + (10)²

     = 156.25

=> AB = 12.5 cm.

Hence perimeter of rhombus = 4 * Side = 4 * 12.5 = 50 cm.