Question

8. The diagonals of a rhombus measure 16 cm and 30 cm. Find its perimeter.​

Answer 1

Answer:

Diagonals intersect at 90° angles

Taking Rhombus ABCD. Diagonals intersect at O.

All 4 triangles formed thus, are congruent.

In triangle AOB, AO2+BO2=AB2

Since diagonals bisect each other,

AO=1/2 of AC, =16/2=8.

BO=1/2 of BD, =30/2=15.

8*8 + 15*15 = AB2

64+225=AB2

289=AB2

AB=√289=17

All 4 sides are equal.

Therefore perimeter is 4*side which is 17*4=68.

Answer is 68 cm.