Statement 1: A rhombus shaped sheet with perimeter 40 cm has one diagonal 12 cm and the other diagonal is 16 cm. Statement 2: If the other diagonal of this rhombus = x cm, x = 102 - 62. 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, The perimeter of a rhombus = 40 cm. One diagonal = 12 cm. As we know, the perimeter of the rhombus = 4 x side ⇒ 4 x side = 40 cm ⇒ side = cm ⇒ side = 10 cm Let ABCD be a rhombus. From figure, AB = 10 cm Let diagonal AC = 12 cm We know that, Diagonals of rhombus bisect each other. Then, OA = OC = = 6 cm Let OB be a cm. Since the diagonal of a rhombus bisect at 90°. Applying pythagoras theorem in triangle AOB, we get: ⇒ AB2 = OA2 + OB2 ⇒ (10)2 = (6)2 + a2 ⇒ a2 = (10)2 - (6)2 ⇒ a2 = 100 - 36 ⇒ a2 = 64 ⇒ a = ⇒ a = 8 So, OB = 8 cm BD = 2 x OB = 2 x 8 cm = 16 cm. ∴ Statement 1 is true. As solved above, If the other diagonal of this rhombus = x cm, Then will be equal to 102 - 62. ∴ Statement 2 is false. ∴ Statement 1 is true, and statement 2 is false. Hence, option 3 is the correct option.

Mathematics

Statement 1: A rhombus shaped sheet with perimeter 40 cm has one diagonal 12 cm and the other diagonal is 16 cm.
Statement 2: If the other diagonal of this rhombus = x cm, x = 10² - 6².
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.

Mensuration

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Mathematics

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Mathematics

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If the area of a trapezium is 32 cm2 and distance between its parallel sides is 8 cm; the sum of length of its parallel side is :4 cm16 cm8 cm12 cm

Assertion (A): If BC = 14 cm, AB = 14 x 4 cmReason (R): AB = 4 x 2r = 4 x 14 cmA 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.

If the area of a trapezium is 32 cm² and distance between its parallel sides is 8 cm; the sum of length of its parallel side is :
4 cm
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Assertion (A): If BC = 14 cm, AB = 14 x 4 cm
Reason (R): AB = 4 x 2r = 4 x 14 cm
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.