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Question (21)

QN0019632

Two squares of sides 9 units and 12 units form a combined square of side:

(A) 13 units
(B) 15 units
(C) 17 units
(D) 21 units

Correct Answer: B

Explanation:

c² = 9² + 12² = 81 + 144 = 225, so c = 15.

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Question (22)

QN0019633

If the areas of two squares are 81 sq. units and 225 sq. units, the combined square has area:

(A) 144 sq. units
(B) 225 sq. units
(C) 306 sq. units
(D) 729 sq. units

Correct Answer: C

Explanation:

81 + 225 = 306 sq. units.

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Question (23)

QN0019634

The congruent figures T, U, W and X in the construction help show that:

(A) The figure is circular
(B) All sides are equal
(C) The figure is rectangular
(D) The figure is triangular

Correct Answer: B

Explanation:

Congruent figures imply equal corresponding sides.

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Question (24)

QN0019635

Two squares have sides 20 units and 21 units. The side of the combined square is:

(A) 28 units
(B) 29 units
(C) 30 units
(D) 41 units

Correct Answer: B

Explanation:

c² = 20² + 21² = 400 + 441 = 841, so c = 29.

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Question (25)

QN0019636

If two squares have areas 16 sq. units and 9 sq. units, the combined square has side:

(A) 4 units
(B) 5 units
(C) 6 units
(D) 7 units

Correct Answer: B

Explanation:

Total area = 25 sq. units, so side = 5 units.

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Question (26)

QN0019637

The area relation for combining two different squares is:

(A) a + b = c
(B) a² + b² = c²
(C) ab = c²
(D) a² − b² = c²

Correct Answer: B

Explanation:

The square on the hypotenuse equals the sum of the squares on the other sides.

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Question (27)

QN0019638

If one square has side 12 units and the combined square has side 13 units, the other square has side:

(A) 3 units
(B) 4 units
(C) 5 units
(D) 7 units

Correct Answer: C

Explanation:

13² − 12² = 169 − 144 = 25, so the side is 5 units.

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Question (28)

QN0019639

The square formed on the hypotenuse of a right triangle has area equal to:

(A) Product of the areas on the sides
(B) Difference of the areas on the sides
(C) Sum of the areas on the sides
(D) Half the sum of the areas

Correct Answer: C

Explanation:

This is Baudhāyana’s theorem.

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Question (29)

QN0019640

Two squares have areas 64 sq. units and 225 sq. units. The side of the combined square is:

(A) 15 units
(B) 16 units
(C) 17 units
(D) 19 units

Correct Answer: C

Explanation:

Total area = 289 sq. units, so side = 17 units.

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Question (30)

QN0019641

The right triangle used in Baudhāyana’s construction is formed using:

(A) The areas of the squares
(B) The perimeters of the squares
(C) The side lengths of the squares
(D) The diagonals of the squares

Correct Answer: C

Explanation:

The sides of the two squares form the perpendicular sides of the triangle.

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Question (21)

Two squares of sides 9 units and 12 units form a combined square of side:

Explanation:

Link:

Question (22)

If the areas of two squares are 81 sq. units and 225 sq. units, the combined square has area:

Explanation:

Link:

Question (23)

The congruent figures T, U, W and X in the construction help show that:

Explanation:

Link:

Question (24)

Two squares have sides 20 units and 21 units. The side of the combined square is:

Explanation:

Link:

Question (25)

If two squares have areas 16 sq. units and 9 sq. units, the combined square has side:

Explanation:

Link:

Question (26)

The area relation for combining two different squares is:

Explanation:

Link:

Question (27)

If one square has side 12 units and the combined square has side 13 units, the other square has side:

Explanation:

Link:

Question (28)

The square formed on the hypotenuse of a right triangle has area equal to:

Explanation:

Link:

Question (29)

Two squares have areas 64 sq. units and 225 sq. units. The side of the combined square is:

Explanation:

Link:

Question (30)

The right triangle used in Baudhāyana’s construction is formed using:

Explanation:

Link:

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