Question

The perimeter of a rectangular board is $70$ cm. If the area of rectangular board is $300$ cm${}^2$; find the length.

• A. $20$ cm
• B. $10$ cm
• C. $30$ cm
• D. $35$ cm

Answer 1

The correct option is A $20$ cm

Perimeter of a rectangular board is $70$ cm.
Length $=$ $x$ cm.
$\therefore 2($ width $+x)=70$
$\Rightarrow$ width $=\frac{70-2x}{2}$
$\Rightarrow$width $=(35-x)$ cm
Area $=$ $300c{m}^2$
$\Rightarrow x(35-x)=300$
$\Rightarrow 35x-x^2-300=0$
$\Rightarrow x^2-35x+300=0$
$\Rightarrow x^2-15x-20x+300=0$
$\Rightarrow x(x-15)-20(x-15)=0$
$\Rightarrow (x-15)(x-20)=0$
$\Rightarrow x=15$, $x=20$
Width=$35-15$, Width=$35-20$
$=$ $20$ cm, $=$ $15$ cm