Question

A rectangular paper, when folded in to two congruent parts had a perimeter of $34$ cm for each part folded along in one set of sides and the same was $38$ cm 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. None of these

Answer 1

The correct option is A $140c{m}^2$

when folded along the breadth then
$2(\frac{l}{2}+b)=34$
$(l+2b)=34$ ........................(1)
when folded along the length,then
$2(l+\frac{b}{2})=38$
$(2l+b)=38$ .................(2)
multiply the (1) by 2 and subtracts from (2)
$3b=30\Rightarrow b=10$
Substitute the value of $b$ in (1)
$\Rightarrow l+2\times 10=34$
$\Rightarrow l=34-20\Rightarrow 14$
Hence area of paper=$10\times 14=140sq.cm$