Question

6) Parul has a piece of land which is in the shape of a rhombus (see fig.) She wants her
daughter and 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 diagonal is 160 m,
how much area each of them will get for their crops?
100 m
B
100 m
160 m
100 m
с
D
100 m
azium are 60 cm and 77 cm and other sides are 25 cm and 26​

Answer 1

Given:-

• Perimeter of land=400m
• Diagonal of land=160m

To Find:-

• Area for daughter and son=?

Solution:-

• At first we have to calculate the side of rhombus with the help of given perimeter than calculate the area of triangle by applying formula of heron's and semiperimeter.]

As , we know that in rhombus all sides are equal to eachother so, let the side be x and also assume that ABCD is a rhombus, all sides are AB ,CD, BC, AD

Perimeter of rhombus=4×side

=>4×x=400

=>4x=400

=>x=100m

Now calculate here area of triangle and it's semiperimeter here,]

=>Semiperimeter=a+b+c/2

• Here a=100, b=100 c=160

=>semiperimeter=100+100+160/2

=>semiperimeter=360/2=180m

• Now calculate area of triangle]

=>Area=√s(s-a)(s-b)(s-c)

=>Area=√180(180-100)(180-100)(180-160)

=>Area=√180×80×80×20

=>Area=√23040000

=>Area=4800m²

• If notice in the rhombus that both son and daughter got equal piece of land to grow different types of crop. It means the area of their land also will be same]

Hence,

• Area for daughter=4800m²
• Area for son=4800m²

Answer 2

Perimeter of land=400m

Diagonal of land=160m

so,

perimeter of land=4×s

perimeter=4s

4s=400

s=100m

Semiperimeter=a+b+c/2

=>100+100+160/2

=>360/2

=>180

Area=√s(s-a)(s-b)(s-c)

• by solving we get here,

Area=4800m²

therefore,

Area of daughter=4800m²

Area of son=4800m²