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MCQ

In the given figure, X is a point in the interior of square ABCD. AXYZ is also a square. If DY = 3 cm and AZ = 2 cm, then BY =

#### Options

5 cm

6 cm

7 cm

8 cm

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#### Solution

In the following figure we are given

DY = 3cm

AZ = 2cm

Where ABCD is a square and AXYZ is also a square

We are asked to find *BY*

From the above figure we have XY=YZ=AZ=AX

Now in the given figure

DZ = DY + YZ

= 3+2

= 5cm

So,

`AD = sqrt(DZ^2 + AZ^2)`

` = sqrt(25 + 4)`

` = sqrt 29 cm`

Now inn triangle ΔAXB

`BX = sqrt(AB^2 - AX^2)`

` = sqrt(29 - 4)`

= 5cm

So

BY = XY + BX

= 2 + 5

= 7 cm

Concept: Congruence of Triangles

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