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 = $\dfrac{40}{4}$ 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 = $\dfrac{12}{2}$ = 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 = $\sqrt{64}$

⇒ 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 $\dfrac{x}{2}$ 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.