Statement 1: ABCD is a rhombus, its diagonal AC = 16 cm and diagonal BD = 12 cm, perimeter of rhombus = 64 cm. Statement 2: OA = 8 cm, OB = 6 cm. Then, AB = 10 cm And, perimeter of rhombus = 40 cm 1. Both the statements are true. 2. Both the statements are false. 3. Statement 1 is true, and statement 2 is false. 4. Statement 1 is false, and statement 2 is true.

Given, ABCD is a rhombus, diagonal AC = 16 cm and diagonal BD = 12 cm. The diagonals of a rhombus bisect each other at right angles. ∴ ∠AOB = 90° Each diagonal is divided into two equal segments. ∴ AC = 16 cm ⇒ AO = OC = = 8 cm ∴ BD = 12 cm ⇒ BO = OD = = 6 cm According to Pythagoras theorem, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. ⇒ Hypotenuse2 = Base2 + Height2 In Δ AOB, ⇒ AB2 = BO2 + OA2 ⇒ AB2 = 62 + 82 ⇒ AB2 = 36 + 64 ⇒ AB2 = 100 ⇒ AB = ⇒ AB = 10 cm According to formula, perimeter of rhombus = 4 x length of side = 4 x 10 = 40 cm. ∴ Statement 1 is false, and statement 2 is true. Hence, option 4 is the correct option.

Mathematics

Statement 1: ABCD is a rhombus, its diagonal AC = 16 cm and diagonal BD = 12 cm, perimeter of rhombus = 64 cm.
Statement 2: OA = 8 cm, OB = 6 cm. Then, AB = 10 cm
And, perimeter of rhombus = 40 cm
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.

Pythagoras Theorem

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Mathematics

Pythagoras Theorem

Related Questions

Angle AOB is:
60°
90°
45°
none of these

Assertion (A): Angle BOC = 90°.
Reason (R): OC² = 3² + 4² = 25
OB² = 6² + 8² = 100
OC² + OB² = 125 = BC²
A is true, but R is false.
A is false, but R is true.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, and R is the incorrect reason for A.

Mathematics

Pythagoras Theorem

Related Questions

Angle AOB is:60°90°45°none of these

Assertion (A): Angle BOC = 90°.Reason (R): OC2 = 32 + 42 = 25OB2 = 62 + 82 = 100OC2 + OB2 = 125 = BC2A is true, but R is false.A is false, but R is true.Both A and R are true, and R is the correct reason for A.Both A and R are true, and R is the incorrect reason for A.

Angle AOB is:
60°
90°
45°
none of these

Assertion (A): Angle BOC = 90°.
Reason (R): OC² = 3² + 4² = 25
OB² = 6² + 8² = 100
OC² + OB² = 125 = BC²
A is true, but R is false.
A is false, but R is true.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, and R is the incorrect reason for A.