Question

One side of a rectangular field is $200$ cm and one of its diagonal is $250$ cm. Find the area of the field.

• A. $50000$ cm
• B. $60000$ cm
• C. $30000$ cm
• D. $40000$ cm

Answer 1

Answer: (C)

$30000$ cm

Let $ABCD$ be a rectangular field and $AC$ is diagonal.

So, $AC=250cm$ and $BC=200cm$

In right-angled $△ABC,$

$\Rightarrow$ $(AC{)}^2=(AB{)}^2+(BC{)}^2$

$\Rightarrow$ $(250{)}^2=(AB{)}^2+(200{)}^2$

$\Rightarrow$ $62500=(AB{)}^2+40000$

$\Rightarrow$ $(AB{)}^2=22500$

$\therefore$ $AB=150cm$

$\Rightarrow$ Area of rectangular field $ABCD=AB\times BC$

$=150\times 200$

$=30000c{m}^2$