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.
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm
Answers
Answer:
c. 7cm
I hope it will help you.
- 7 cm .
Given :- In figure X is a point in the interior of square ABCD, AXYZ is also a square. DY = 3 cm and AZ = 2 cm .
To Find :- BY = ?
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm
Concept used :-
- Pythagoras theorem in a right angled triangle says that :- (Perpendicular)² + (Base)² = (Hypotenuse)² .
- Each angle of square is equal to 90° and all sides are equal in measure .
Solution :-
In square AXYZ,
→ AZ = 2 cm { given }
So,
→ AX = YX = ZY = 2 cm { All sides of square are equal in measure } ---------- Equation (1)
also,
→ DY = 3 cm
then,
→ ZY + YD = 2 + 3 { from Equation (1) }
→ ZD = 5 cm
now, in right angled ∆AZD, { Right angle at Z since AXYZ is square . }
→ AZ = Base = 2 cm
→ ZD = Perpendicular = 5 cm
→ AD = Hypotenuse .
So, using pythagoras theorem we get,
→ (Hypotenuse)² = (Perpendicular)² + (Base)²
→ AD² = ZD² + AZ²
→ AD² = 5² + 2²
→ AD² = 25 + 4
→ AD² = 29
→ AD = √29 cm
now, in square ABCD,
→ AD = √29 cm
So,
→ AB = BC = CD = √29 cm { Each side of square is equal in measure . } --------- Equation (2)
Now, in right angled ∆AXB,
→ AB = Hypotenuse = √29 cm { From Equation (2) }
→ AX = Perpendicular = 2 cm { From Equation (1) }
→ XB = Base .
again, using pythagoras theorem we get,
→ (Hypotenuse)² = (Perpendicular)² + (Base)²
→ AB² = AX² + XB²
→ (√29)² = 2² + XB²
→ 29 = 4 + XB²
→ XB² = 29 - 4
→ XB² = 25
→ XB = √25
→ XB = 5 cm { Since negative value is not possible . }
therefore,
→ BY = YX + XB
→ BY = 2 + 5
→ BY = 7 cm (Ans.)
Hence, Length of BY is equal to (c) 7 cm .
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