Question

The ratio of the diagonals of a rhombus is 4:5 . If area of it is 1000 cm^2 , find the length of both diagonals.

Answer 1

Answer:

area of rhombus is equal to (d1×d2)÷2

let D1 is equal to 4x

and d2 is equal to 5 x

so, (d1×d2)÷2

(4x×5x)÷2=1000

(20x^2)÷2=1000

10x^2=1000

1000÷10=x^2

100=x^2

x=10

Suddi 1 is equal to 4 into

Answer 2

The lengths of the diagonals are 40 cm and 50 cm

Given:

The ratio of the diagonals of a rhombus is 4: 5  

The area of the rhombus is 1000 cm²  

To find:

Find the length of both diagonals.  

Solution:

Formula used:

Area of Rhombus = (d₁ × d₂)/2  

From the data,

The ratio of the diagonals of a rhombus is 4: 5  

Let 4x and 5x be the diagonals of the rhombus

[ Since they are in 4: 5 ratio]

Using the formula,

Area of Rhombus = (4x × 5x)/2  

= 20x²/2 = 10x²

It is given that area of the rhombus = 1000 cm²  

=> 10x² = 1000 cm²

=> x² = 100

=> x = √100

=> x = 10 cm  

The lengths of diagonals can be calculated as follows

=> 4x  = 4(10) = 40 cm

=> 5x = 5(10) = 50 cm

Therefore,

The lengths of the diagonals are 40 cm and 50 cm

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