Question

perimeter of a rectangle is 34cm .if its breadth is of 5. cm ,find the length of each diagonal of it (through pythagoras theoram)

Answer 1

Given:

The perimeter of a rectangle is 34 cm

Its breadth is of 5. cm

To find:

The length of each diagonal of it (through Pythagoras theorem)

Solution:

The formulas to be used:

$\boxed{\bold{Perimeter\:of \:a rectangle = 2[L + B]}}\\\\\boxed{\bold{Diagonal\:of \:a rectangle, D^2 = L^2 + B^2}}$

Let's assume,

"L" → represents the length of the rectangle

"B" → represents the breadth of the rectangle = 5 cm

The perimeter of the rectangle = 34 cm

∴ $2[L + B] = 34$

substituting the value of B = 5 cm, we get

$\implies 2 [L + 5] = 34$

$\implies L + 5 = 17$

$\implies L = 17 - 5$

$\implies \bold{L = 12}$

∴ Each diagonal of the rectangle is,

= $\sqrt{L^2 + B^2} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13\:cm$

Thus, the length of each diagonal of the rectangle is → 13 cm.

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Answer 2

Answer:

Given:

The perimeter of a rectangle is 34 cm

Its breadth is of 5. cm

To find:

The length of each diagonal of it (through Pythagoras theorem)

Solution:

The formulas to be used:

\begin{gathered}\boxed{\bold{Perimeter\:of \:a rectangle = 2[L + B]}}\\\\\boxed{\bold{Diagonal\:of \:a rectangle, D^2 = L^2 + B^2}}\end{gathered}

Perimeterofarectangle=2[L+B]

Diagonalofarectangle,D

2

=L

2

+B

2

Let's assume,

"L" → represents the length of the rectangle

"B" → represents the breadth of the rectangle = 5 cm

The perimeter of the rectangle = 34 cm

∴ 2[L + B] = 342[L+B]=34

substituting the value of B = 5 cm, we get

\implies 2 [L + 5] = 34⟹2[L+5]=34

\implies L + 5 = 17⟹L+5=17

\implies L = 17 - 5⟹L=17−5

\implies \bold{L = 12}⟹L=12

∴ Each diagonal of the rectangle is,

= \sqrt{L^2 + B^2} = \sqrt{12^2 + 5^2} = \sqrt{144 + 25} = \sqrt{169} = 13\:cm

L

2

+B

2

=

12

2

+5

2

=

144+25

=

169

=13cm

Thus, the length of each diagonal of the rectangle is → 13 cm.