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Question (1)

QN0029433

A square has side length 7 cm. A new square is constructed on its diagonal. What is the area of the new square?

(A) 49 cm²
(B) 98 cm²
(C) 56 cm²
(D) 196 cm²

Correct Answer: B

Explanation:

Area of original square = 7² = 49 cm². The square on the diagonal has double the area, i.e., 98 cm².

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Question (2)

QN0029434

A square of area 72 cm² is cut to form a square of half its area. What is the area of the smaller square?

(A) 18 cm²
(B) 24 cm²
(C) 36 cm²
(D) 48 cm²

Correct Answer: C

Explanation:

The required square has half the area of the original square. Half of 72 cm² = 36 cm².

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Question (3)

QN0029435

The diagonal of a square is 10 cm. Which statement is correct?

(A) The area of the square is 100 cm²
(B) The area of the square is 50 cm²
(C) The side length is 10 cm
(D) The side length is 5 cm

Correct Answer: B

Explanation:

Area of a square in terms of diagonal d is d²/2. Thus, area = 10²/2 = 50 cm².

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Question (4)

QN0029436

An isosceles right triangle has equal sides of length 5 cm. Between which two integers does its hypotenuse lie?

(A) 5 and 6
(B) 6 and 7
(C) 7 and 8
(D) 8 and 9

Correct Answer: C

Explanation:

Hypotenuse = √(2 × 5²) = √50. Since 7² < 50 < 8², the hypotenuse lies between 7 and 8.

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Question (5)

QN0029437

The hypotenuse of an isosceles right triangle is √98 units. Each equal side is

(A) 5 units
(B) 6 units
(C) 7 units
(D) 8 units

Correct Answer: C

Explanation:

For an isosceles right triangle, c² = 2a². So, 98 = 2a² ⇒ a² = 49 ⇒ a = 7 units.

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Question (6)

QN0029438

Two squares have sides 6 cm and 8 cm. The side of the square whose area equals the sum of their areas is

(A) 10 cm
(B) 12 cm
(C) 14 cm
(D) 15 cm

Correct Answer: A

Explanation:

Required side = √(6² + 8²) = √100 = 10 cm.

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Question (7)

QN0029439

A right triangle has sides 9 cm, 12 cm and 15 cm. Which statement is true?

(A) It is not a right triangle
(B) It is a primitive Baudhāyana triple
(C) It is a scaled version of (3,4,5)
(D) None of these

Correct Answer: C

Explanation:

(9,12,15) = 3 × (3,4,5), so it is a scaled version of the primitive triple (3,4,5).

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Question (8)

QN0029440

Which of the following is a primitive Baudhāyana triple?

(A) (6, 8, 10)
(B) (10, 24, 26)
(C) (8, 15, 17)
(D) (15, 36, 39)

Correct Answer: C

Explanation:

The numbers 8, 15 and 17 have no common factor greater than 1, so the triple is primitive.

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Question (9)

QN0029441

A right triangle has one shorter side 20 cm and hypotenuse 29 cm. The other shorter side is

(A) 19 cm
(B) 20 cm
(C) 21 cm
(D) 22 cm

Correct Answer: C

Explanation:

Other side² = 29² – 20² = 841 – 400 = 441. Hence, the side is 21 cm.

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Question (10)

QN0029442

The diagonal of a square is 6√2 cm. Its side length is

(A) 3 cm
(B) 6 cm
(C) 3√2 cm
(D) 12 cm

Correct Answer: B

Explanation:

Diagonal = side × √2. Therefore, side = 6√2/√2 = 6 cm.

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Question (1)

A square has side length 7 cm. A new square is constructed on its diagonal. What is the area of the new square?

Explanation:

Link:

Question (2)

A square of area 72 cm² is cut to form a square of half its area. What is the area of the smaller square?

Explanation:

Link:

Question (3)

The diagonal of a square is 10 cm. Which statement is correct?

Explanation:

Link:

Question (4)

An isosceles right triangle has equal sides of length 5 cm. Between which two integers does its hypotenuse lie?

Explanation:

Link:

Question (5)

The hypotenuse of an isosceles right triangle is √98 units. Each equal side is

Explanation:

Link:

Question (6)

Two squares have sides 6 cm and 8 cm. The side of the square whose area equals the sum of their areas is

Explanation:

Link:

Question (7)

A right triangle has sides 9 cm, 12 cm and 15 cm. Which statement is true?

Explanation:

Link:

Question (8)

Which of the following is a primitive Baudhāyana triple?

Explanation:

Link:

Question (9)

A right triangle has one shorter side 20 cm and hypotenuse 29 cm. The other shorter side is

Explanation:

Link:

Question (10)

The diagonal of a square is 6√2 cm. Its side length is

Explanation:

Link:

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