Question

If the diagonals of the rhombus are in the ratio 4:7 and the area is 504sqcm find the length of the diagonals​

Answer 1

Answer:

• The diagonals are 24 cm and 42 cm.

Step-by-step explanation:

Given that:

• The diagonals of the rhombus are in the ratio 4 : 7 and the area is 504 sq. cm.

To Find:

• The length of the diagonals.

Let us assume:

• Smaller diagonal be 4x.
• Bigger diagonal be 7x.

Formula used:

• Area of a rhombus = (D₁ × D₂)/2

Where,

• D₁ = Smaller diagonal of the rhombus
• D₂ = Bigger diagonal of the rhombus

Finding the diagonals:

⟿ (4x × 7x)/2 = 504

⟿ 28x² = 504 × 2

⟿ 28x² = 1008

⟿ x² = 1008/28

⟿ x² = 36

⟿ x² = 6²

⟿ x = 6

∴ Diagonals are:

Smaller diagonal = 4x = (4 × 6) = 24 cm

Bigger diagonal = 7x = (7 × 6) = 42 cm

Answer 2

Answer:

Diagonals are 24 cm and 42 cm.

Step-by-step explanation:

Given :

Diagonals of the rhombus are in the ratio 4 : 7 and the area is 504 cm²

To find :

Length of the diagonals.

Solution :

We know,

• $Area\;of\;rhombus\;= \frac{Diagonal_1*Diagonal_2}{2}$

Let the diagonals be,

• 4x and 7x

We have,

• Area = 504 cm²

Substituting,

• $504\;=\;\frac{4x*7x}{2}$

• $504\;=\frac{28x^2}{2}$

Cross multiply,

• $1008\;=\;28x^2$

• $x^2\;=\;\frac{1008}{28}$

• $x^2\;=36$

• $x = \sqrt{36}$

• $x = 6$

Diagonals are,

• 4x = 24 cm
• 7x = 42 cm