Question

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 land and produce different crops to suffice the needs of their family. She divided the land in two equal parts. If the perimeter of the land is $400m$ and one of the diagonals is $160m$, the area of each part is

• A. 8800 m²
• B. 4800 m²
• C. 48000 m²
• D. 88000 m²

Answer 1

Answer: (B)

Let $ABCD$ is the field.

each side be $x$.

Perimeter of the field $=4x$.

Given perimeter $=400m$

$\Rightarrow 4x=400m$

$\Rightarrow x=100m$

Length of the diagonal $BD=160m$

$\Rightarrow$ In $\Delta ABD$

$AB=a=100m,AD=b=100m$ and $BD=c=160m$

$\Rightarrow s=\frac{a+b+c}{2}=\frac{100+100+160}{2}=180m$

$s-a=180-100=80m$

$s-b=180-100=80m$

$s-c=180-160=20m$

Area of $\Delta ABD=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{180m\times 80m\times 80m\times 20m}$

$=\sqrt{9\times 20\times 80\times 80\times 20}{m}^2$

$=3\times 20\times 80m^2$

$=4800m^2$

Since, $ABCD$ is a rhombus and diagonal divides it into two congruent triangles.

Therefore, each of them will get an area $4800m^2$.