Question

One of the diagonals of a rhombus is 12cm and its area is 54cm2.The perimeter of the rhombus is *

Answer 1

Answer:

perimeter = 30 cm

Step-by-step explanation:

area of rhombus = ½ × d1 × d2 = 54 cm²

one diagonal = d1 = 12 cm

let the other diagonal be = x

$\frac{1}{2} \times 12 \times x = 54 \\ 6x = 54 \\ x = \frac{54}{6} = 9$

the other diagonal = 9 cm

diagonal of rhombus bisects each other perpendicularly

it is divided into four right angled triangle

diagonal 1 => 1/2 × 12 = 6

diagonal 2 => 1/2 × 9 = 4.5

therefore the adjacent sides of right angle are 6cm and 4.5 cm

using Pythagoras theory we find the hypotenuse ( side of rhombus)

${(hyp)}^{2} = {6}^{2} + {(4.5)}^{2} \\ {(hyp)}^{2} = 36 + 20.25 \\ {(hyp)}^{2} = 56.25 \\ hyp = \sqrt{50.25} \\ hyp = 7.5cm$

therefore the side of rhombus is = s = 7.5 cm

perimeter of rhombus = 4 x s

all sides of rhombus are equal

7.5 × 4 = 30 cm

the perimeter of rhombus is = 30 cm

hope you get your answer

Answer 2

Answer:

perimeter = 30 cm

Step-by-step explanation:

area of rhombus = ½ × d1 × d2 = 54 cm²

one diagonal = d1 = 12 cm

let the other diagonal be = x

the other diagonal = 9 cm

diagonal of rhombus bisects each other perpendicularly

it is divided into four right angled triangle

diagonal 1 => 1/2 × 12 = 6

diagonal 2 => 1/2 × 9 = 4.5

therefore the adjacent sides of right angle are 6cm and 4.5 cm

using Pythagoras theory we find the hypotenuse ( side of rhombus)

therefore the side of rhombus is = s = 7.5 cm

perimeter of rhombus = 4 x s

all sides of rhombus are equal

7.5 × 4 = 30 cm

the perimeter of rhombus is = 30 cm

hope you get your answer