Question

The perimeter of a rectangular board is 70 cm. Taking its length as x cm, find its width in terms of x.
If the area of the rectangular board is $300c{m}^2$, find its dimensions.

• A. Width = (35 - x) cm; 20 cm and 15 cm
• B. Width = (70 - x) cm; 30 cm and 15 cm
• C. Width = (45 - x) cm; 20 cm and 10 cm
• D. Width = (35 - x) cm; 10 cm and 30 cm

Answer 1

The correct option is A Width = (35 - x) cm; 20 cm and 15 cm

Perimeter of the rectangle=$70$cm
Length of the rectangle=$x$cm
We know,
Perimeter of the rectangle=$2(length+breadth)$
$=>70=2(x+breadth)$
$=>\frac{70}{2}=x+breadth$
$=>x+breadth=35$
$=>breadth=35-x$
Given,area of rectangular board=$30c{m}^2$
$=>length+breadth=300$
$=>x(35-x)=300$
$=>-x^2+35x-300=0$
$=>x^2-35x+300=0$
$=>x^2-20x-15x+300=0$
$=>x(x-20)-15(x-20)=0$
$=>(x-20)(x-15)=0$
$\therefore x-20=0$ or $x-15=0$
$=>x=20$ or $x=15$
$\therefore 35-x=35-20$ or $\therefore 35-x=35-15$
$=15$ or $=20$
$\therefore$Dimensions are $15$ and $20$cm