Question

The diagonals of a rhombus measures 8cm and 6cm. What is the length of a side of the rhombus? Please help me it's very urgent Show working

Answer 1

Given :

• The diagonal of a rhombus measures 8 cm and 6 cm.

To find :

• Length of a single of the rhombus.

Solution :

• 1st Diagonal = 8 cm
• 2nd Diagonal = 6 cm

The diagonals devide the rhombus into 4 congruent right triangles.

Each side of the rhombus is the hypotenuse of one triangle.

So,

Each leg of one of those triangles is half of one diagonal.

According to the attachment ,

• AB = Side of rhombus
• AC = 8 cm
• BD = 6 cm

Therefore,

BO = 6/2 = 3 cm

AO = 8/2 = 4 cm

∆ AOB is a right triangle.

According to Pythagoras theorem ,

AB² = AO² + BO²

→ AB² = 4² + 3²

→ AB² = 16+9

→ AB = √25

→ AB = 5

Therefore, the length of the side of the rhombus is 5 cm.

Answer 2

Fig. of question ⬆⬆⬆⬆⬆⬆⬆⬆

$\mathcal{\huge{\underline{\underline{\red{Question ?}}}}}$

✳ The diagonals of a rhombus measures 8cm and 6cm. What is the length of a side of the rhombus?

$\mathcal{\huge{\underline{\underline{\green{Answer:-}}}}}$

✒ The length of a side of the rhombus is 5cm.

$\mathcal{\huge{\underline{\underline{\blue {Solution:-}}}}}$

⚾ According to the question ,

⭐ The, Diagonal 6cm = 6/2 = 3.The two legs of right triangle within rhombus. 

⭐ The, Diagonal 8cm = 8/2 = 4. The two legs of right triangle within rhombus. 

⚽ Applying the, Pythagorean Theorem,

We know diagonals bisects at right angle

∴ In △AOD ,

⇒AO² + OD² = AD²

⇒3² + 4² = AD²

⇒9 + 16 = AD²

⇒25 = AD²

⇒√25 =AD

➡ AD=5cm ✅✅

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