Question

In 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 find BY.
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Answer 1

Answer:

BY=7cm

Step-by-step explanation:

this is a question from IOM by silverzone olympiad right

Answer 2

Answer:

7cm

Step-by-step explanation:

Given:- ABCD and AXYZ are squares

DY= 3cm

AZ=2cm

To find:- BY

Solution:-

In ΔZDA, It is a right-angled triangle

∠Z=90°

DZ=ZY+DY

    =2+3

    =5cm

By Pythagoras theorem

$DZ^{2}$ + $AZ^{2}$ = $AD^{2}$

5² + 2² = 29

AD=√29

In ΔAXB, it is a right-angled triangle

AB=√29 (∵ΔABCD is a square)

By Pythagoras theorem

AX² + XB² = AB²

Let XB= $x$

AX² +$x$² = AB²

2² +$x^{2}$ = 29

$x^{2}$ =29-4=25

$x$ = 5

BY = BX+XY

BY= 5+2

    =7cm

∴BY = 7cm