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Last updated at May 29, 2018 by Teachoo

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Example 6 Sanya has a piece of land which is in the shape of a rhombus She wants her one daughter and one son to work on the land and produce different crops. She divided the land in two equal parts. If the perimeter of the land is 400 m and one of the diagonals is 160 m, how much area each of them will get for their crops? Let the piece of land be ABCD It is Given that Diagonal = 160 m BD = 160 m. Also, Perimeter = 400 m AB + BC + CD + AD = 400 m ๐ฅ + ๐ฅ + ๐ฅ + ๐ฅ = 400 m 4x = 400 Now we have to find Area each will get, i.e. Area of ฮ ADB & ฮ BCD For ฮABD , Area of triangle = โ(s(sโa)(sโb)(s โc)) Here, s is the semi-perimeter, and a, b, c are the sides of the triangle Here, a= 100 m , b = 100 m , c = 160 m Area of ฮ ABD =โ(๐ (๐ โ๐)(๐ โ๐)(๐ โ๐)) Putting a= 100 m , b = 100 m , c = 160 m ,s = 180 m = โ(180(180 โ100)(180 โ100)(180 โ160)) = โ(180ร80ร80ร20) m2 = โ((18ร8ร8ร2)ร(10)4) m2 = โ(36ร(8ร8)ร(10)4) = โ(62ร(82)ร(10)4) = โ((6)2) ร โ((82) ) ร โ((104) ) = 6 ร 8 ร ใ(104)ใ^(1/2) = 6 ร 8 ร 102 = 6 ร 8 ร 100 = 4800 m2 Thus, Area ฮABD = 4800 m2 Similarly, Area ฮBCD = 4800 m2 Thus, Area of son = 4800 m2 and Area of daughter = 4800 m2.

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.