Question

In a rhombus, the two diagonals are in the ratio 4:5. If its area is 490 cm square.,length of the smaller diagonal is :​

Answer 1

Step-by-step explanation:

area of rhombus= ½× D¹× D²

490= ½× 4x× 5x

980= 20x²

x= 7

diagonal are = 4× 7= 28

and = 5× 7= 35

(D¹= diagonal 1

D²= diagonal 2)

Answer 2

The length of the smaller diagonal is 28 cm.

Step-by-step explanation:

Consider the provided information.

The two diagonals are in the ratio 4:5.

The length of two diagonals must be 4x and 5x.

Area of rhombus is: $A=\frac{pq}{2}$

Where p and q are the diagonals of the rhombus.

Now substitute p=4x, q=5x and A=490 in above formula.

$490=\frac{(4x)(5x)}{2}$

$980=20x^2$

$x^2=49$

$x=\pm7$

The value of x can't be a negative number.

Therefore the value of x=7.

Thus the length of two diagonals are:

$4x=4\times7=28$

$5x=5\times7=35$

Hence, the length of the smaller diagonal is 28 cm.

#Learn more

The length of one of the diagonals of a rhombus is 5 cm less than the lenght of the other diagonal .the area of the rhombus is 33 cm sq. . find the length of each diagonal .​

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