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.

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

Diagonal 1=

Diagonal 2=

147 = ½ *

Multiply both side by 2

294 =

294 = 6

Divide both side by 6

294/6 = 6/6

49 =

= 7 unit

b

step-by-step explanation:

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step-by-step explanation: