Question

The area of a square and a rectangular field is equal and is $900$ $c{m}^2$ If the perimeter of the rectangular field is $2$ m more than that of the square field calculate the dimensions of the rectangular field

• A. $24$ m, $10$ m
• B. $30$ m, $25$ m
• C. $36$ m, $25$ m
• D. $36$ m, $24$ m

Answer 1

The correct option is C $36$ m, $25$ m

Let side of square$=am$

Length of rectangle$=lm$

Breadth of rectangle$=bm$

Now, $a^2=900$cm^2$\Rightarrow a=30cm$ & $lb=900c{m}^2\to 1$

And, $2(l+b)=4a+2=4\times 30+2=122m$

$l+b=61m$

From $1$,$lb=900\Rightarrow b=\frac{900}{l}$

$\Rightarrow l+\frac{900}{l}=61\Rightarrow l^2-61l+900=0$

$l^2-36l-25l+900=0\Rightarrow (l-36)(l-25)=0$

$\Rightarrow l=36,25$

$\therefore l=36,b=25$