Question

If the lengths of two diagonals of a rhombus are 12 cm and 16 cm , then the length of each side of the rhombus are​

Answer 1

Step-by-step explanation:

as we know that area of a rhombus can be written as = D1 × D2/2

also we know that diagonals are 12 and 16

so

=> 12×16/2 = 96 cm²

now > area is 96 cm² but it is also clear that diagonals of rhombus intersect each other at mid point

therefore 4 triangle will be formed

which has two sides of leghth 6 and 8

(6and 8 bcoz diagonals meets at mid point)

now area of a triangle = 96 /4 = 24

therefore third side of triangle will be=>

√6²+4² = third side

= √36+16 =

Answer 2

Answer : 10 cm

EXPLANATION :

diagonals divide rhombus into 4 equal right angaled triangles .

whose perpendicular = 12÷ 2= 6cm

and base = 16÷2 = 8cm

and the diagnoal is the side of rhombus

$using \: pgt \: {h}^{2} = {p}^{2} + {b}^{2}$

h = ( 6*2 + 8*2)*1/2

(36 + 64)*1/2

100*1/2 = 10cm