Question

The length of the diagonal of a rectangle is 34 cm and breadth is
30 cm. Find the perimeter of the rectangle.
S
34 cm
R
30 cm​

Answer 1

Answer:

92 cm

Step-by-step explanation:

Diagonal² = length² + breadth²

because it is right angled triangle

34² = L ² + 30²

1156 - 900= L²

256 = L²

Length = 16 cm

Perimeter = 2(l+b)

2(16+30)

2 (46)

92cm

Answer 2

Given:

• Length of the diagonal = 34 cm.

• Breadth = 30 cm.

To calculate:

• Perimeter of the rectangle.

Calculation:

Here, we have to find the perimeter of the rectangle. Formula to calculate the perimeter of the rectangle is :

• $\underline{\boxed{\sf{{Perimeter}_{(Rectangle)} = 2 ( length + breadth) }}}$

Basically, we have to find the length too. So, let us calculate the length through the formula of diagonal.

As we know that,

• $\underline{\boxed{\sf{{Diagonal}_{(Rectangle)} = \sqrt{ length + breadth} }}}$

[ By the pythagoras property, we derived the formula of diagonal.]

Also, we can write it as :

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf {\dashrightarrow {Diagonal}^{2} = {Length}^{2} + {Breadth}^{2} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Now, substituting values:

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf {\dashrightarrow {34}^{2} = {Length}^{2} + {30}^{2} }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf {\dashrightarrow {Length}^{2} = {34}^{2} - {30}^{2} \: cm}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf {\dashrightarrow {Length}^{2} = 1156-900 \: cm }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf {\dashrightarrow {Length}^{2} = 256 \: cm }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf {\dashrightarrow Length = \sqrt{256} \: cm }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\boxed{\sf {\dashrightarrow Length = 16 \: cm }}$

Now, substituting the values of breadth and length in the formula of perimeter of the rectangle.

• $\underline{\boxed{\sf{{Perimeter}_{(Rectangle)} = 2 ( length + breadth) }}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf {\dashrightarrow {Perimeter}_{(Rectangle)} = 2 ( 16 + 30 ) \: cm }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf {\dashrightarrow {Perimeter}_{(Rectangle)} = 2 ( 46 ) \: cm }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\boxed{\sf {\dashrightarrow {Perimeter}_{(Rectangle)} = 92 \: cm }}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Therefore, perimeter of the rectangle is 92 cm.

Required Answer:

• Perimeter of rectangle ⇒ 92 cm