The length of diagonals of a rhombus are in the ratio 8 : 15 and area

1.	The length of diagonals of a rhombus are in the ratio 8 : 15 and area are 240 cm2 then find the side of the rhombus.1. 17 cm2. 20 cm3. 18 cm4. 21 cm
Answer» Correct Answer - Option 1 : 17 cm Given: Area of the Rhombus = 240 cm2 Formula used: Area of Rhombus = (d1 × d2)/2 Area of Rhombus = Side × Altitude d12 + d22 = 4 × s2 Here, d1, d2, and s are diagonals and side of rhombus respectively. Concept used: All sides of a rhombus are equal and diagonals bisect each other at a right angle. Calculation: Let the diagonals be 8x and 15x Area of Rhombus = (d1 × d2)/2 ⇒ 240 = (8x × 15x)/2 ⇒ x = 2 Then our diagonals are 16 cm and 30 cm Now, d12 + d22 = 4 × s2 ⇒ 162 + 302 = 4 × s2 ⇒ s2 = 289 ⇒ s = 17 cm ∴ The side of the rhombus is 17 cm

The length of diagonals of a rhombus are in the ratio 8 : 15 and area are 240 cm2 then find the side of the rhombus.1. 17 cm2. 20 cm3. 18 cm4. 21 cm

Answer» Correct Answer - Option 1 : 17 cm

Given:

Area of the Rhombus = 240 cm2

Formula used:

Area of Rhombus = (d1 × d2)/2

Area of Rhombus = Side × Altitude

d12 + d22 = 4 × s2

Here, d1, d2, and s are diagonals and side of rhombus respectively.

Concept used:

All sides of a rhombus are equal and diagonals bisect each other at a right angle.

Calculation:

Let the diagonals be 8x and 15x

Area of Rhombus = (d1 × d2)/2

⇒ 240 = (8x × 15x)/2

⇒ x = 2

Then our diagonals are 16 cm and 30 cm

Now, d12 + d22 = 4 × s2

⇒ 162 + 302 = 4 × s2

⇒ s2 = 289

⇒ s = 17 cm

∴ The side of the rhombus is 17 cm

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