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Question (31)

QN0019642

If two squares have sides 1 unit and 1 unit, the combined square has side:

(A) 1
(B) √2
(C) 2
(D) 4

Correct Answer: B

Explanation:

c² = 1² + 1² = 2, so c = √2.

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Question (32)

QN0019643

A combined square has area 625 sq. units. If one original square has area 49 sq. units, the other has area:

(A) 525 sq. units
(B) 576 sq. units
(C) 600 sq. units
(D) 625 sq. units

Correct Answer: B

Explanation:

625 − 49 = 576 sq. units.

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Question (33)

QN0019644

In the construction, the angles of the new four-sided figure are right angles because:

(A) Adjacent angles add up to 90°
(B) Adjacent angles add up to 180°
(C) All angles are equal to 60°
(D) Opposite angles are unequal

Correct Answer: A

Explanation:

The adjacent angles formed are complementary and sum to 90°.

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Question (34)

QN0019645

If squares have sides 11 units and 60 units, the side of the combined square is:

(A) 61 units
(B) 71 units
(C) 121 units
(D) 3600 units

Correct Answer: A

Explanation:

c² = 11² + 60² = 3721, so c = 61.

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Question (35)

QN0019646

The square on the hypotenuse of sides 8 units and 6 units has area:

(A) 14 sq. units
(B) 48 sq. units
(C) 64 sq. units
(D) 100 sq. units

Correct Answer: D

Explanation:

Area = 8² + 6² = 64 + 36 = 100 sq. units.

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Question (36)

QN0019647

The method of combining two different squares leads directly to which theorem?

(A) Midpoint Theorem
(B) Baudhāyana-Pythagoras Theorem
(C) Angle Sum Theorem
(D) Intercept Theorem

Correct Answer: B

Explanation:

This construction explains the Baudhāyana-Pythagoras Theorem.

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Question (37)

QN0019648

If two squares have sides 16 units and 30 units, the side of the combined square is:

(A) 32 units
(B) 34 units
(C) 36 units
(D) 46 units

Correct Answer: B

Explanation:

c² = 16² + 30² = 1156, so c = 34.

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Question (38)

QN0019649

The diagonal used in Baudhāyana’s construction belongs to a:

(A) Rectangle
(B) Circle
(C) Pentagon
(D) Trapezium

Correct Answer: A

Explanation:

The diagonal of the rectangle forms the side of the new square.

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Question (39)

QN0019650

Two squares of areas 100 sq. units and 225 sq. units combine to form a square of side:

(A) 15 units
(B) 18 units
(C) 20 units
(D) 25 units

Correct Answer: B

Explanation:

Total area = 325 sq. units and side = √325 = 5√13 ≈ 18.03 units.

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Question (40)

QN0019651

If squares have sides 28 units and 45 units, the side of the combined square is:

(A) 53 units
(B) 63 units
(C) 73 units
(D) 83 units

Correct Answer: A

Explanation:

c² = 28² + 45² = 2809, so c = 53.

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Question (31)

If two squares have sides 1 unit and 1 unit, the combined square has side:

Explanation:

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Question (32)

A combined square has area 625 sq. units. If one original square has area 49 sq. units, the other has area:

Explanation:

Link:

Question (33)

In the construction, the angles of the new four-sided figure are right angles because:

Explanation:

Link:

Question (34)

If squares have sides 11 units and 60 units, the side of the combined square is:

Explanation:

Link:

Question (35)

The square on the hypotenuse of sides 8 units and 6 units has area:

Explanation:

Link:

Question (36)

The method of combining two different squares leads directly to which theorem?

Explanation:

Link:

Question (37)

If two squares have sides 16 units and 30 units, the side of the combined square is:

Explanation:

Link:

Question (38)

The diagonal used in Baudhāyana’s construction belongs to a:

Explanation:

Link:

Question (39)

Two squares of areas 100 sq. units and 225 sq. units combine to form a square of side:

Explanation:

Link:

Question (40)

If squares have sides 28 units and 45 units, the side of the combined square is:

Explanation:

Link:

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