Question

9. If the length of a diagonal of a square is 20 cm, find: a. side of the square b. perimeter of the square​

Answer 1

Answer:

(a). √10 cm

(b). 4√10 cm

Step-by-step explanation:

a). Side of square = √(diagonal of square )/√2

Hence side of square = √10 cm

perimeter of square = 4× side of square = 4√10

Answer 2

$\Large \underline{ \underline \text{Question:}}$

If the length of a diagonal of a square is 20cm. find:

• a. Side of the square.

• b. Perimeter of the square.

$\Large \underline{ \underline \text{Solution:}}$

Finding the length of sides of square,

As given,

• $\text{Diagonal of square }{= 20cm}$

As we know that,

• $\boxed{ \text{Diagonal of square }= \sqrt{2} \times \text{Length}_{ \text{(Side)}}}$

So we can say that,

$\cdot \cdot \cdot \longrightarrow 20cm= \sqrt{2} \times \text{Length}_{ \text{(Side)}}$

$\cdot \cdot \cdot \longrightarrow \frac{20 cm}{ \sqrt{2} }= \text{Length}_{ \text{(Side)}}$

$\cdot \cdot \cdot \longrightarrow \frac{20 cm}{ \sqrt{2} } \times \frac{ \sqrt{2} }{ \sqrt{2} } = \text{Length}_{ \text{(Side)}}$

$\cdot \cdot \cdot \longrightarrow \frac{20 \sqrt{2} cm}{ 2 } = \text{Length}_{ \text{(Side)}}$

We get,

$\cdot \cdot \cdot \longrightarrow \boxed{\text{Length}_{ \text{(Side)}} = 10 \sqrt{2}cm}$

Hence,

• The length of side of square is 10√2cm.

.

Finding the perimeter of square,

We find,

• The side of square is 10√2cm long.

As we know that,

• Perimeter of square = 4(Side)

Let substitute the value,

• ➺ Perimeter of square = 4(10√2cm)
• ➺ Perimeter of square = 40√2cm

Therefore,

• The perimeter of square is 40√2cm.

.

$\Large \underline{ \underline \text{Required Answer:}}$

• The length of side of square is 10√2cm.

• The perimeter of square is 40√2cm.