Question

A rectangle with 12 cm & 4 cm, reformed into a Rhombus. Both diagonals of Rhombus are equal & one of its angle is 60°. Find the Area of Newly formed Rhombus.
(a) 24√ 3
(b) 16 √3
(c). 32 √3
(d) 8 √3​

Answer 1

Answer:

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Answer 2

Let a & b are length of diagonal then

a+b=12 ________ (1) (Given)

perimeter of diagonal =2a2+b2 ______ (2) Given

85=2a2+b2

45=a2+b2

on squaring both sides we get

(45)2=(a2+b2)2

80=a2+b2 _________ (3)

using equation (1) we have

80=a2+(12−a)2

80=a2+144+a2−24a

2a2−24a+64=0

a2−12a+32=0

a2−8a−4a+32=0

a(a−8)−4(a−8)=0

(a−4)(a−8)=0

[a=4  or a=8]

from equation (1) [b=8 or 4]