Question

please tell me ??????​

Answer 1

Question

4. Each side of rhombus is 61 cm and one of its diagonal is 22 cm. Find the length of the Other diagonal and the area of the Rhombus.

Given

• Each side of rhombus = 61 cm
• One of its diagonal = 22 cm

To find

• Length of the other diagonal
• Area of the rhombus

Solution

To find the length of the other diagonal, we will use the pythagoras theorem. As we know, that the diagonals of a rhombus bisect each other at 90°. So, for that we will take one triangle and half the diagonal.

Figure [Refer to the attached image.]

In △QOR

OQ = 22/2 = 11 cm

• OQ = 11 cm

By using pythagoras theorem,

H² = P² + B²

where,

• H = Hypotenuse (The longest side.)
• P = Perpendicular
• B = Base

⟼ QR² = OQ² + OR²

⟼ (61)² = (11)² + OR²

• Using identity :-

• (a - b)(a + b) = a² - b²

⟼ 61² - 11² = OR²

⟼ (61 - 11)(61 + 11) = OR²

⟼ (40)(72) = OR²

⟼ 3600 = OR²

⟼ √3600 = OR

⟼ ± 60 Reject - ve = OR

⟼ OR = 60 cm

⟼ PR = 2 × OR

⟼ PR = 2 × 60

⟼ PR = 120 cm

∴ Length of the other diagonal (PR) = 120 cm.

Now, finding the area of the rhombus :-

Using formula,

★ Area of rhombus = 1/2 × First diagonal × Second diagonal

Substituting the given values,

⟼ Area of rhombus = 1/2 × 22 × 120

⟼ Area of rhombus = 11 × 120

⟼ Area of rhombus = 1320

∴ Area of the rhombus (PQRS) = 1320 cm².

Answer 2

Answer:

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Step-by-step explanation:

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