Question

two sticks of lengths 3m and 5m are crossing each other such that longer stick bisect shorter stick at 90 degree. Which shape the is formed by joining their end points?(square,rectangle, rhombus,kite)​

Answer 1

Given :- Length of two sticks is 3 m and 5m and they are crossing each other such that longer stick bisect shorter stick at 90 degree.

To Find :- Which shape the is formed by joining their end points ?

A) square

B) rectangle

C) rhombus

D) kite .

Solution :-

given that, length of both sticks is different as 3 m and 5m and only longer stick bisect shorter stick .

Now we know that,

• In a parallelogram both diagonals bisect each other .

so, checking given options ,

A) Square = A parallelogram whose all sides are equal and both diagonals bisect each other . Therefore, this shape is not possible .

B) Rectangle = A parallelogram whose opposite sides are equal and both diagonals bisect each other . Therefore, this shape is not possible .

C) Rhombus = A parallelogram whose all sides are equal and both diagonals bisect each other at 90° . But since we have given that, that longer stick bisect shorter stick . Therefore, this shape is not possible .

D) kite = A quadrilateral whose diagonals are perpendicular (90°) and longer diagonal bisect shorter diagonal only .

since we have given that, both sticks cross each other at 90° and longer stick bisect shorter stick .

therefore, we can conclude that, the shape formed by joining the end points of sticks of 3m and 5m will form a (D) kite .

Extra :-

some properties of kite :-

• Adjacent sides are equal .
• Only one pair of opposite angle is equal .
• Diagonals are perpendicular and longer diagonal also bisect shorter diagonal .
• Area = (1/2) * D1 * D2 { where D1 and D2 are diagonals. }

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Answer 2

Given : two sticks of lengths 3m and 5m are crossing each other such that longer stick bisect shorter stick at 90 degree.

To Find :  Which shape the is formed by joining their end points?

square

rectangle

rhombus

kite

Solution:

two sticks of lengths 3m and 5m   will be the diagonals of the Quadrilateral formed.

Square and rectangle has Equal Diagonal Length

Hence Square and rectangle are not possible

now  when Diagonals  bisects each other perpendicularly then Rhombus is formed

When  Diagonals intersects each other perpendicularly and the longer diagonal bisect shorter diagonal then KITE shape is formed  

As here mentioned that :

longer stick bisect shorter stick at 90 degree

Hence  the longer diagonal bisect shorter diagonal perpendicularly  hence  KITE shape is formed  

If longer stick is also bisected then RHOMBUS shape will be formed

As nothing is mentioned about bisection of longer stick  hence assuming generalized case

Hence KITE Shape will be formed

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