Question

Find the length of the shorter diagonal of a rhombus if:

(a) The length of the longer diagonal is 15 and the area is 90.

(b) The lengths of the diagonals are in the ratio of 2:3 and the area of the rhombus is 147.

Answer 1

a) Area of rhombus = ½ * (diagonal1)*(diagonal 2)

Let diagonal (D2 )= longer diagonal = 15 and diagonal (D1) = shorter diagonal

90 = ½ (D1)*15

90 = 7.5 D1

Now divide both side by 7.5

90/7.5 = d1

D1= 12 units.

b) Area of rhombus = ½ * (diagonal1)*(diagonal 2)

Let the ratio be
`x`

Diagonal 1=
`2x`

Diagonal 2=
`3x`

147 = ½ *
`(2x)*(3x)`

Multiply both side by 2

294 =
`(2x)*(3x)`

294 = 6
`x^2`

Divide both side by 6

294/6 = 6
`x^2`/6

49 =
`x^2`

`x`= 7 unit