Question

In the given diagram, $ABCD$ is a rectangle. $ADEF,DCHG,BCLM$ and $ABNO$ are four squares. If the perimeter of $ABCD$ is $16$ cm and total area of the four squares is $68c{m}^2$, then what is the area of $ABCD$?

• A. $20c{m}^2$
• B. $15c{m}^2$
• C. $18c{m}^2$
• D. $12c{m}^2$

Answer 1

The correct option is B $15c{m}^2$

$2(a+b)=16㎝\Rightarrow a+b=8cm\to 1$

Also let side of the square be ${}^{\prime }{x}^{\prime }cm$

$\therefore 4\times x^2=68\Rightarrow x^2=17\Rightarrow x=\sqrt{17}$

Also, $x=b\therefore b=\sqrt{17}$

$\therefore a+\sqrt{17}=8\Rightarrow a=(8-\sqrt{17})$

Now, area ABCD$=a\times b=(8\times \sqrt{17})\times \sqrt{17}$

$=8\sqrt{17}-17$

$=32-17$$=15c{m}^2$