Question

The length of rectangle $R$ is $10$ more than the side of square $S$ The width of the rectangle is $10$ less than the side of the square. What the ratio of the areas, $R$ and $S$?

• A. $99:100$
• B. $101:100$
• C. $1:1$
• D. $199:200$

Answer 1

The correct option is A $99:100$

Let side of square be ${}^{\prime }{a}^{\prime }$ Now

Area of square, $s=a^2$

Let length and breadth of rectangle be l and b respactively.

Then, $l=a+10$ & $b=a-10$

Area of rectangle $=l\times b$ = $1.1a\times 0.9a=0.99a^2$

$R=0.99$$a^2$

$\therefore$ $\frac{R}{S}=\frac{{0.99a}^2}{a^2}=\frac{0.99}{1}=\frac{99}{100}=99:100$