Question

Suman has a piece of land ,which is in the shape of a rhombus. She wants her two sons to work on the land and produce different crops. She divides the land in two equal parts by drawing a diagonal. If its each side is 100m and one of the diagonals is of length 120m, how much area each of them will get for crops?​

Answer 1

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

Note: Whenever we face such types of problems the key concept is to use Heron’s