Question

The sides of rectangle are all produced in order in such a way that the length of each side is increased by $k$ times itself. The area of the new quadrilateral formed becomes $2\frac{1}{2}$ times the area of the original rectangle. Find the approx value of $k$

• A. $1.58$
• B. $\frac{5}{2}$
• C. $\frac{3}{2}$
• D. None of these

Answer 1

The correct option is A $1.58$

Let length of rectangle be 'l' and breadth be 'b'

Area of rectangle$=l\times b$

New length$=kl$

New breadth$=kb$

New area$=k^2\left(lb\right)$

$\Rightarrow k^2\left(lb\right)=\frac{5}{2}\times lb\Rightarrow k^2=\frac{5}{2}$

$\Rightarrow k=\sqrt{\frac{5}{2}}=\sqrt{2.5}\approx 1.58$