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 divide the land in two equal parts of the perimeter of the land is 400m and one of diagonal is 160m how much area each of them will get for their crops
Question Answers Related Questions Sanya has a piece of land which is in the shape of 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 400m and one of the diagonals is 160 m, how much area each of them will get for their crops. Answer VerifiedVerified 98.4K+ Views Hint: In this question, we have to find the area of the triangle formed by the diagonals of the rhombus. As we know that all the sides of the rhombus are equal and the area of any triangle with the given sides can be found by using the Heron’s formula: s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√ square unit. WhereSissemi−perimeteranda,b,carethelengthsofthesides. We also know that semi-perimeter is s=a+b+c2 Complete step-by-step answer: As the lengths of sides of the rhombus are equal, we can find the length of each side by the given perimeter To find the length of side of a rhombus, we have to use the formula i.e., perimeter4 Therefore, the length of side of the rhombus is 4004 ⇒100m We also know that one diagonal of rhombus divides it in two equal parts and we get a triangle Therefore, a=100,b=100&c=160 i.e., lengths of sides of triangle are 100m,100m and 160m Find the semi-perimeter: To find the area of the triangle with the sides 100m,100m and 160m, we can use the Heron’s formula i.e., s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√ square unit. ⇒180(180−160)(180−100)(180−100−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√⇒180(20)(80)(80)−−−−−−−−−−−−−√⇒Δ=4800 Where$△$=Areaofthetriangle Hence, answer is 4800 m2
