Question

Length of one diagonal of rhombus is twice of the other, area is 25 cm²,length of the shortest diagonal​

Answer 1

Answer:

• Length of shortest diagonal is 5cm.

Step-by-step explanation:

Given:

• Length of one diagonal of rhombus is twice of the other, area is 25 cm².

To Find:

• Length of the shortest diagonal.

Solution:

• Let shortest diagonal be x cm
• Longest diagonal be 2x cm

Area of rhombus = 1/2 × d₁ × d₂

➞ 25 cm² = 1/2 × x × 2x

➞ 25 cm² = 1/2 × 2x²

➞ (25)² = x²

➞ x = √25

➞ x = 5 cm

Hence,

• Shortest diagonal = 5cm
• Longest diagonal = 5 × 2 = 10 cm.

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Answer 2

Answer:

The length of the shortest diagonal is:-

➵ 5 centimetres

Step-by-step explanation:

Given:-

The area of the rhombus is 25 cm²

Length of one Diagonal of rhombus is twice of the other

To find:-

The length of the shortest diagonal

Solution:-

The area of the rhombus is clearly given to us as 25 cm² and we have to find the shortest diagonal of the rhombus

And a hint to solve this question is the one Diagonal is twice the other

Let the diagonal be ' x '

Other diagonal will be ' 2x '

As we know that the area of the rhombus is :-

⇶ (Product of it's Diagonals)/2

Using the formula:-

∴ Area of the rhombus = ( p q )/2

⇒ 25 = ( x × 2x )/2

⇒ 25 = 2x² / 2

⇒ 2(25) = 2x²

⇒ 50 = 2x²

⇒ x² = 50/2

⇒ x² = 25

⇒ x = √25

⇒ x = 5

The value of x we got as 5 cm

Now we can easily find the diagonals of the rhombus using the value of x :-

One Diagonal is x

➾ 5 cm

Other Diagonal is 2x

➾ 2(5cm)

⇒ 10 cm

We can clearly see that 5 cm is the shortest diagonal

Answer:-

Hence, The length of the shortest diagonal is 5 cm.