Question

A rectangular paper when folded into two congruent parts has a perimeter of $34cm$ for each part folded along one set of sides and the same is $38cm$ when folded along the other set of sides. What is the area of the paper ?

• A. $140c{m}^2$
• B. $240c{m}^2$
• C. $560c{m}^2$
• D. $646c{m}^2$

Answer 1

Answer: (A)

$140c{m}^2$

When folded along the breadth we have,
$2(\frac{1}{2}+b)=34$
$\Rightarrow l+2b=34$ ...(i)
When folded along the length, we have
$2(l+\frac{b}{2})=38$
$\Rightarrow 2l+b=38$ ....(ii)
From (i), we have
$l=34-2b$
Putting in (ii)
$2(34-2b)+b=38$

$\Rightarrow 68-4b+b=38$
$\Rightarrow 68-3b=38$

$\Rightarrow 3b=30$

$\Rightarrow b=10cm$
Now, $l+20=34$ ...from (i)

$\Rightarrow l=14cm$
$\therefore$ Area of paper $=l\times b=14\times 10$$=140c{m}^2$