Question

Two line segments, each $9cm$ long, bisect each other at right angles. Their end points are joined together. The shape formed is a:

• A. Square
• B. Kite
• C. Trapezium
• D. rhombus

Answer 1

The correct option is A Square

Let $PS$ and $QR$ are the two line segments, each of $9$cm, and bisect each other at right angles.

By joining the end points of these line, we get a shape given in the figure.

In $△POQ$, $\angle POQ={90}^o$, $OP=OQ=4.5$

By using Pythagoras theorem,

$P{Q}^2=O{P}^2+O{Q}^2$

$=(4.5{)}^2+(4.5{)}^2=40.5$

$\therefore PQ=6.36$

Similarly, $QS=6.36=RS=PS$

Thus, length of all sides is same and all angles are right angle.

Hence, the shape formed is square.