Question

Digonal of rhumbus mesure 8cm and 6cm find its parimeter

Answer 1

QUESTION

Diagonal of a rhombus measure 8cm and 6cm find its perimeter.

Answer

Let PQRS is a rhombus

so...PQRS is a rhombus and we know that all four sides of a rhombus are of equal length. 

And, In Δ POQ 

PQ is hypotenuse, OP is base and OQ is perpendicular.

Using Pythagoras Theorem -

⇒ (PQ)² = (OP)² + (OQ)²

⇒ (PQ)² = (3)² + (4)²

⇒ (PQ)² = 9 + 16

⇒ (PQ)² = 25

⇒ PQ = √25

⇒ PQ = 5 cm

So, length of each side of the given rhombus is 5 cm.

Perimeter of rhombus = 4 × side 

⇒ 4 × 5

= 20 cm

So, perimeter of the rhombus PQRS is 20 cm.


Thank you

@Be Brainly

Answer 2

Given :

Diagonals of a rhombus which are 8 cm and 6 cm , then half of the diagonals = 4 cm and 3 cm respectively .

As , we know the diagonals of the rhombus are perpendicular bisectors , so the triangle so formed will be right triangle .

So, we can use the property of the right triangle which is Pythagoras theorem .

${hypotenuse}^{2} = {base}^{2} + {perpendicular}^{2} \\ {h}^{2} = {4}^{2} + {3}^{2} \\ \: \: = 16 + 9 \: \: \: = 25 \\ {h}^{2} = 25 \\ h = \sqrt{25 } \\ 5cm$
Now , we have side , then put it in formula for having perimeter .
$perimeter \: of \: a \: rhombus = 4 \times side \\ = 4 \times 5 \\ 20cm$
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