Question

The perimeter of a rhombus is 40 cm and the length of one diagonal is 16 cm. Find the length of the other diagonal

Answer 1

Answer:12 cm

Step-by-step explanation: let, ABCD be the rhombus and the diagonals AC and BD intersect at point O. Let, AC=16cm

∵the sides of a rhombus are equal

∴the perimeter of a rhombus = 4*length of side

i.e perimeter of ABCD = 40 cm

∴AB=10 cm

Now, ΔAOB is a right triangle with ∠AOB=90° (∵diagonals of rhombus bisect each other at right angles)

In ΔAOB we get.

AO²+OB²=AB² (PYTHAGORAS THEOREM)

⇒8²+OB²=10² (AO=1/2*AC)

⇒OB²=100-64

⇒OB²=36

⇒OB=6

∴Length of diagonal BD =2*OB=12 cm

i.e length of the other diagonal=12cm

(NOTE:draw the figure as explained to understand it better. )