Question

Find the perimeter of a rhombus the length of whose diagonal are 16 cm and 30 cm

Answer 1

Answer:

68 cm

Step-by-step explanation:

The diagonals bisect each other and meet at right angles.

So the divide the rhombus into 4 right angled triangles, with each side of the rhombus being the hypotenuse of one of the triangles.  The leg of each triangle are:

16 cm / 2 = 8 cm    and    30 cm / 2 = 15 cm.

So by Pythagoras' Theorem, the hypotenuse (a side of the rhombus) is:

√( 8² + 15² ) = √( 64 + 225 ) = √289 = 17 cm.

The perimeter of the rhombus is then the sum of the four sides:

perimeter = 4 × 17 cm = 68 cm