Question

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

• A. 140 cm²
• B. 240 cm²
• C. 560 cm²
• D. 490 cm²
• E. None of these

Answer 1

The correct option is A

140 cm²

When folded along its breadth, we have:
$2\left(\frac{1}{2}+b\right)$ = 34 ⇒ l + 2b = 34 ..........(i)
When folded along its length, we have:
2$\left(l+\frac{b}{2}\right)$ = 38 ⇒ 2l + b = 38 ..........(ii)
Solving (i) and (ii), we get $\Rightarrow$ l = 14 and b = 10
$\therefore$ Area of the paper = (14 $\times$ 10) cm${}^2$ = 140 cm${}^2$