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Q.

The perimeter of rhombus with one diagonal 24 cm long is the same as the perimeter of an equilateral triangle with side 20 cm. Find the length of the other diagonal?

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a

18

b

20

c

25

d

5

answer is A.

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Detailed Solution

We have side of triangle = 20 cm
Perimeter of triangle = 60 cm
Perimeter of rhombus = 60 cm
⇒ 4 × side of rhombus
⇒ a = 15 cm
Diagonal = 24 cm
Diagonal = 12 cm + 12 cm
a = 15 cm
⇒ 152 = 122 + x2
⇒ x2 = 81
⇒ x = 9
Diagonal = 2 × legs of right triangle
rhombus = 2 × 9 = 18 cm.
Hence option (1) is correct.

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The perimeter of rhombus with one diagonal 24 cm long is the same as the perimeter of an equilateral triangle with side 20 cm. Find the length of the other diagonal?