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  • The lengths of the sides of a cyclic quadrilateral are in the ratio 3 : 4 : 5 : 6 and its perimeter is 36 m. Then the area of the cyclic quadrilateral is (in m2) 

The lengths of the sides of a cyclic quadrilateral are in the ratio 3 : 4 : 5 : 6 and its perimeter is 36 m. Then the area of the cyclic quadrilateral is (in m2) 

Option: 1

24\sqrt6


Option: 2

30\sqrt2


Option: 3

24\sqrt{10}


Option: 4

None of these


Answers (1)

best_answer

Given that the lengths of the sides of a cyclic quadrilateral are in the ratio 3 : 4 : 5 : 6, Also perimeter is 36 m

3x + 4x+ 5x + 6x = 36

18x = 36

x = 2

sdes are 6, 8, 10 and 12

\\s=\frac{6+8+10+12}{2}=18

Area of cyclic quadrilateral 

\\=\sqrt{(18-6)(18-8)(18-10)(18-12)}\\=\sqrt{6\times 8\times 10\times 12}=24\sqrt{10} 

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