Question

what is the formula of finding sides of rhombus when its diognals are given​

Answer 1

Answer:

Rhombus is a quadrilateral whose all sides are of same length.

Now, we have rhombus ABCD with side length a ( unknown value) and diagonals d1d1 and d2d2 (known values)

Then, we have the relation:

a=d21+d22√2a=d12+d222

This is obtained from the fact that the diagonals of a rhombus bisect at right angles.

Let, the diagonals AC (d1)(d1) and BD (d2)(d2) meet at center I.

Then in ΔAID,∆AID,

AI=d12;IDd22;AD=aAI=d12;IDd22;AD=a

Using Pythagoras theorem:

AD2=AI2+ID2AD2=AI2+ID2

⇒a2=(d12)2+(d22)2⇒a2=(d12)2+(d22)2

⇒a=(d12)2+(d22)2−−−−−−−−−−−√=d21+d22√2⇒a=(d12)2+(d22)2=d12+d222

Step-by-step explanation:

hope its help you dear