Question

The diagonals of a rhombus are in ratio 6:8. If it's perimeter is 100 cm, find the length of its shorter diagonal.?​

Answer 1

Correct Question :

• The diagonals of a rhombus are in ratio 6:8. If it's Area is 100 cm², find the length of its shorter diagonal.?

Answer :

• Shorter diagonal = 12 cm

S O L U T I O N :

Let, the diagonal of rhombus be 6x and 8x.

We know that,

Area of rhombus = ¹/2 × D1 × D2

Here,

• D1 = Shorter diagonal
• D2 = Larger diagonal

[ Put the values ]

⇒ 100 = ¹/2 × 6x × 8x

⇒ 100 = 3x × 8x

⇒ 100 = 24x²

⇒ x = √100/24

⇒ x = √4.1

⇒ x = 2 cm

Now,

★ Shorter diagonal,

⇒ 6x

⇒ 6 × 2

⇒ 12 cm

★ Larger diagonal,

⇒ 8x

⇒ 8 × 2

⇒ 16 cm

Therefore,

The length of its shorter diagonal is 12 cm.

Answer 2

Correct Question:-

• The diagonals of a rhombus are in ratio 6:8. If it's area is 100 cm², find the length of its shorter diagonal.

⠀

Given:-

• Diagonal of a rhombus are in the ratio of 6:8.
• It's area is 100 cm².

⠀

To find:-

• Length of its shorter diagonal.

⠀

Solution:-

• Let the ratio of diagonals be x.

⠀

$\tt\longrightarrow{}$ Bigger diagonal = 8x

$\tt\longrightarrow{}$ Shorter diagonal = 6x

⠀

★Formula used:-

$\star{\boxed{\sf{\orange{Area\: of\: rhombus = \dfrac{1}{2} \times D1 \times D2}}}}$

⠀

Here,

• D1 = Bigger diagonal
• D2 = Shorter diagonal

⠀

★Putting values:-

$\large{\tt{\longmapsto{Area = 100}}}$

⠀

$\large{\tt{\longmapsto{\dfrac{1}{2} \times 8x \times 6x = 100}}}$

⠀

$\large{\tt{\longmapsto{4x \times 6x = 100}}}$

⠀

$\large{\tt{\longmapsto{24x^2 = 100}}}$

⠀

$\large{\tt{\longmapsto{x^2 = \dfrac{100}{24}}}}$

⠀

$\large{\tt{\longmapsto{x^2 = 4.16}}}$

⠀

$\large{\tt{\longmapsto{x = \sqrt 4.16}}}$

⠀

$\large{\tt{\longmapsto{\boxed{\red{x = 2.04}}}}}$

⠀

Hence,

• Shorter diagonal = 6x
• = 6 × 2.04
• = 12.24 cm