Question

The diagonals of a rhombus are in ratio 3:4 if the longer diagonal is 12cm then find the are of rhombus​

Answer 1

given diagonals are in the ratio 3:4

therefore we can consider that diagonals be 3x and 4x

  given that

    4x = 3x + 12

therefore x = 12

so, diagonal 1= 3x = 3 . 12 = 36

    diagonal  2 = 4x = 4 . 12= 48

area of rhombus = pq/2   ( when p and q are diagonals)

      hence area of the given triangle = (48+36)/2

                                                            =  42cm^2

Answer 2

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Answer

Let diagonals of arhombusABCD are AC=3k and BD=4k cm.which meet at point O.

Perimeter=4×side

40/4=side

10 cm.=side=AB=BC=CD=DA.

In right angled triangle AOB

OA^2+OB^2=AB^2

(AC/2)^2+(BD)^2=(10)^2

9k^2/4+4k^2=100

(25k^2)/4=100

k^2=16

0k=+/-4

AC=3k=3×4=12cm.

BD=4k=4×4=16cm.

each side =10 cm. ,