Question

The perimeter of thr top of rectangular table is $28m$, whereas its area is $48m^2$. What is the length of its diagonal?

• A. $10$ cm
• B. $12$ cm
• C. $8$ cm
• D. $14$ cm

Answer 1

The correct option is A $10$ cm

$2(x+y)=28m\Rightarrow x+y=14m\to 1$

Also, $x\times y=48m^2\to 2$

From $1,x+y=14\Rightarrow {(x+y)}^2={\left(14\right)}^2=196$

$\Rightarrow x^2+y^2+2xy=196\Rightarrow x^2+y^2+2\times 48=196$

$\Rightarrow x^2+y^2=196-96\Rightarrow x^2+y^2=100$

$\Rightarrow \sqrt{x^2+y^2}=\sqrt{100}\Rightarrow \sqrt{x^2+y^2}=10m$

$\therefore$Length of diagonal$=10m$