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
𝑥 + 𝑥 + 𝑥 + 𝑥 = 400 m
4x = 400
Now we have to find Area each will get,
i.e. Area of Δ ADB & Δ BCD
For ΔABD ,
Area of triangle = √(s(s−a)(s−b)(s −c))
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 Δ ABD =√(𝑠(𝑠 −𝑎)(𝑠 −𝑏)(𝑠 −𝑐))
Putting a= 100 m , b = 100 m , c = 160 m ,s = 180 m
= √(180(180 −100)(180 −100)(180 −160))
= √(180×80×80×20) m2
= √((18×8×8×2)×(10)4) m2
= √(36×(8×8)×(10)4)
= √(62×(82)×(10)4)
= √((6)2) × √((82) ) × √((104) )
= 6 × 8 × 〖(104)〗^(1/2)
= 6 × 8 × 102
= 6 × 8 × 100
= 4800 m2
Thus, Area ΔABD = 4800 m2
Similarly,
Area ΔBCD = 4800 m2
Thus, Area of son = 4800 m2
and Area of daughter = 4800 m2.

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.