Question

the lengths of the diagnols AC and BD of a rhombus are 6cm and 8cm respectively. find the length of each sid.e of a rhombus​

Answer 1

Diagonal 6cm = 3cm + 3cm = legs of right triangle within rhombus. 

Diagonal 8cm = 4cm + 4cm = legs of right triangle within rhombus. 

We need to find the side of the rhombus using the Pythagorean Theorem. 

After that, we use the formula P = 4s to find your perimeter. 

Let s = side of rhombus. 

3^2 + 4^2 = s^2 

9 + 16 = s^2 

25 = s^2 

5 = s 

Answer 2

$\huge\sf\red{Answer:}$

Given:

⇒ The lengths of the diagnols AC and BD of a rhombus are 6cm and 8cm respectively.

Find:

⇒ Find the length of each side of a rhombus.

According to the question:

⇒ AC = 6 cm²

⇒ BD = 8 cm²

Formula:

★ ${\sf{\underline{\boxed{\green{\sf{ Using: 4 \times side^2}}}}}}$

Calculations:

⇒ $\sf 4 \times side^2 = AC^2 + BD^2$

⇒ $\sf 4 \times side^2 = 6^2 + 8^2$

⇒ $\sf Side^2 = 36 + 64$

⇒ $\sf Side^2 = \dfrac{36 + 64}{4}$

⇒ $\sf Side^2 = \dfrac{100}{4}$

⇒ $\sf Side = \sqrt{\dfrac{100}{4}}$

⇒ $\sf Side = \cancel{\dfrac{10}{2}}$

⇒ ${\sf{\underline{\boxed{\green{\sf{ Side = 5 \: cm}}}}}}$

Therefore, 5 cm is length of each side of a rhombus.