Question

18. 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:

$Diagonals are 24 cm and 42 cm.</p><p></p><p>Step-by-step explanation:</p><p></p><p>Given :</p><p></p><p>Diagonals of the rhombus are in the ratio 4 : 7 and the area is 504 cm²</p><p></p><p>To find :</p><p></p><p>Length of the diagonals.</p><p></p><p>Solution :</p><p></p><p>We know,</p><p></p><p>Area\;of\;rhombus\;= \frac{Diagonal_1*Diagonal_2}{2}Areaofrhombus= </p><p>2</p><p>Diagonal </p><p>1</p><p> </p><p> ∗Diagonal </p><p>2</p><p> </p><p> </p><p> </p><p> </p><p>Let the diagonals be,</p><p></p><p>4x and 7x</p><p>We have,</p><p></p><p>Area = 504 cm²</p><p>Substituting,</p><p></p><p>504\;=\;\frac{4x*7x}{2}504= </p><p>2</p><p>4x∗7x</p><p> </p><p> </p><p>504\;=\frac{28x^2}{2}504= </p><p>2</p><p>28x </p><p>2</p><p> </p><p> </p><p> </p><p>Cross multiply,</p><p></p><p>1008\;=\;28x^21008=28x </p><p>2</p><p> </p><p>x^2\;=\;\frac{1008}{28}x </p><p>2</p><p> = </p><p>28</p><p>1008</p><p> </p><p> </p><p>x^2\;=36x </p><p>2</p><p> =36</p><p>x = \sqrt{36}x= </p><p>36</p><p> </p><p> </p><p>x = 6x=6</p><p>Diagonals are,</p><p></p><p>4x = 24 cm</p><p>7x = 42 cm$

Step-by-step explanation:

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}Areaofrhombus=

2

Diagonal

1

∗Diagonal

2

Let the diagonals be,

4x and 7x

We have,

Area = 504 cm²

Substituting,

504\;=\;\frac{4x*7x}{2}504=

2

4x∗7x

504\;=\frac{28x^2}{2}504=

2

28x

2

Cross multiply,

1008\;=\;28x^21008=28x

2

x^2\;=\;\frac{1008}{28}x

2

=

28

1008

x^2\;=36x

2

=36

x = \sqrt{36}x=

36

x = 6x=6

Diagonals are,

4x = 24 cm

7x = 42 cm

Answer 2

Step-by-step explanation:

Let the ratios of diagonal be x then,

(4x*7x)/2 = 504

(28xsq)/2= 504

14xsq = 504

x = sq root of (504/14)

x=sq root of 36

x=6

4x=24

7x=42

hence, the diagonal of the Rhombus are 24cm and 42cm