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:

let first diagonal be 4x and second diagonal be 7x.

Area of rhombus=[(4x)*(7x)]/2

504×2 =28x^2

1008/28=x^2

x^2=36

x=√36

x=6cm

so, diagonals are 6×4=24cm

7×6=42cm

hope it helps u dear☺️☺️☺️

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}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