Question

In an origami class, the diagonal length of a paper plane was measured as given. If the plane was made from the square piece of paper ABDE, find the side length of the square. The side view of the plane is given below:

• A. 200 mm
• B. 750 mm
• C. 500 mm
• D. 250 mm

Answer 1

The correct option is C 500 mm

On unfolding the paper plane, we get,

On comparing △AFC and △EFC, we get,

$\angle AFC=\angle EFC=90°$

$AC=EC=250\sqrt{5}mm$

$FC=FC$

$⟹△AFCand△EFCarecongruentaccordingtoRHScongruencycriterion.$

$⟹AF=EF$

Now, the paper is shaped as a square.

So,
$AE=ED⟹2AF=2EF=ED$

Also,

$ED=FC$

So, on taking AF as x, we get,

$AF=EF=x$
$ED=FC=2x$

On taking △AFC, we get,


On using the Pythagoras theorem, we get,

$A{F}^2+F{C}^2=A{C}^2$
$⟹x^2+(2x{)}^2=(250\sqrt{5}{)}^2$
$⟹5x^2=5\times {250}^2$
$⟹x=250mm$
$⟹AE=ED=2x=500mm$

Hence, the side of square paper is 500 mm.