Question

solve the problem..,. ​

Answer 1

$\underline{\bf{Given\::}}$

• The perimeter of a rhombus is 60 cm. If the length of its longer diagonal measures 24 cm.

$\underline{\bf{Explanation\::}}$

• As we know that formula of the perimeter of rhombus;
• $\boxed{\bf{Perimeter = 4 \times side}}$

A/q

$\mapsto\tt{Perimeter\:of\:rhombus = 4 \times side}$

$\mapsto\tt{60 = 4 \times side}$

$\mapsto\tt{Side = \cancel{60/4}}$

$\mapsto\tt{Side = 15\:cm}$

Therefore,the all side of rhombus will be 15 cm .

• Now, attachment a figure, a/c question:

In ΔOCB :

AC = 24 cm

OC = 1/2 AC

OC = 1/2 × 24

OC = 12 cm

Using by Pythagoras Theorem :-

→ (Hypotenuse)² = (Base)² + (perpendicular)²

→ (BC)² = (OC)² + (OB)²

→ (15)² = (12)² + (OB)²

→ 225 = 144 + 0B²

→ OB² = 225 - 144

→ OB² = 81

→ OB = √81

→ OB = 9 cm

&

BD = 2 × OB

BD = 2 × 9

BD = 18 cm

Thus,

• The shorter diagonal will be 18 cm .

Answer 2

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge \bf \orange{Given -}$

• The perimeter of a rhombus = 60 cm.

• The length of its longer diagonal = 24 cm.

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$\: \: \: \: \: \: \: \: \: \: \: \: \huge \bf \blue{To \: find -}$

• Length of its shorter diagonal.

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$\: \: \: \: \: \: \: \: \: \: \: \: \: \huge\bf \pink{Solution-}$

As we know,

Perimeter=4 × side

= 60 = 4 × side

Side= 60/4

Side = 15cm

•°• All the sides of rhombus measures = 15 cm.

In ΔOBC :

AC = 24 cm

OC = 1/2 AC

OC = 1/2 × 24

OC = 12 cm

Using by Pythagoras Theorem :

= (Hypotenuse)² = (Base)² + (perpendicular)²

= (BC)² = (OC)² + (OB)²

= (15)² = (12)² + (OB)²

= 225 = 144 + 0B²

= OB² = 225 - 144

= OB² = 81

= OB = √81

= OB = 9 cm

BD = 2 × OB

BD = 2 × 9

BD = 18 cm

The shorter diagonal = 18 cm .

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