Question

An insect is located at the edge of a fan blade of length 40 cm. It starts walking towards the centre of the fan. As the insect moves 10 cm from its initial position, the blade has turns through a right angle. The distance between initial and final position now is
A) 80cm
B) 40cm
C) 50cm
D) 10cm
​

Answer 1

40 cm

Step-by-step explanation:

draw a right angle.

mark the angle as angle XYZ

XY=YZ=40cm

now mark 1cm on both XY and YZ from point Y

mark that 1cm as 10 cm both XY and YZ

now join the points which you have marked on XY AND YZ

You get a triangle. Name the triangle as AY

now you have AY=BY=10CM

Find out AB which is the hypotenuse of the triangle AYB.

i.e,

AB^2=AY^2+BY^2

AB^2=10^2+10^2

AB^2=100+100

AB^2=200

THEREFORE,

AB=√200

=40cm

Therefore,the distance between initial and final position of the insect = 40cm

Answer 2

Answer: B) 40cm

The distance between the initial and final position now is B) 40cm

Concept: Distance, Triangles

Formula:

Pythagoras Theorem: $P^{2} +B^{2} =H^{2}$

Step-by-step explanation:

Draw a right angle taking the point of starting of the insect as a corner point

Mark the angle as angle ABC

AB = BC= 40cm(Given)

Mark 1 cm from point B now on both AB and BC.

Mark 1cm as 10 cm for both AB and BC

Now join the points, marked on both cords

You get a triangle.

Name the triangle as XB

Now, XB=YB=10 cm

Find out XY which is the hypotenuse of the triangle XBY

$XY^{2} = XB^{2} + YB^2$

$XY^{2} = 10^{2} + 10^2$

$XY^{2} = 100+100 = 200$

$XY=\sqrt{200}$

XY =40cm

Therefore, the distance between the initial and final position of the insect = 40cm

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