Question

the lenght of one diagonal of a rhombus is less than the second diagonal by 4cm.thearea of the rhombus is 30 sq. cm. find the length of the diagonals

Answer 1

let the length of 1 diagonal be x cm
then , length of another diagonal = x-4 cm

according to question ,


=> area of rhombus = 1/2 × d1 × d2

=> 30 cm² = 1/2 × x × (x-4)

=> 60 = x²-4x

=> x²-4x-60 = 0

=> x²-10x+6x-60 = 0. (by splitting the middle term)


=> x(x-10)+6(x-10) = 0

=> (x+6)(x-10) = 0

=> x+6 = 0

=> x = -6 cm

and

x-10 = 0
=> x = 10 cm


since , length cannot be in negative

hence , length = 10 cm

length of 1st diagonal = x = 10 cm

length of another diagonal = x-4 = 10-4 = 6 cm


hope this helps

Answer 2

IT IS YOUR ANSWER WITH SOLUTION.here x=6
and one side =10