Question

find the length of the diagonal of a rectangle whose length is 15 cm and breadth is 8 cm and find it's perimeter​

Answer 1

$\textbf{\underline{\underline{Answer :-}}}$

$\text{The Diagonal is 17 cm.}$

$\text{Perimeter is 46 cm}$

$\textbf{\underline{\underline{Explanation :-}}}$

$\textsf{\underline{\underline{Given : }}}$

Length of the Rectangle = 15 cm

Breadth of the Rectangle = 8 cm

$\textsf{\underline{\underline{To find :}}}$

The measure of the diagonal

Perimeter of Rectangle

$\textsf{\underline{\underline{Solution :}}}$

Refer the Attachment for better understanding.

In ∆ ACD,

• Base = CD = 15 cm

• Height = AC = 8 cm

• Hypotenuse = AD = x

By Pythagoras Theorem :

$\star$ (Hypotenuse) ² = (Base)² + (Height)²

$\tt{\implies \: {x}^{2} = {15}^{2} + {8}^{2} }$

$\tt{\implies {x}^{2} = 225 + 64 }$

$\tt{\implies {x}^{2} = 289 }$

$\tt{\implies \: x = \sqrt{289} }$

$\tt{\implies \: x = 17}$

$\tt{\implies \: hypotenuse = 17 \: cm}$

$\large{\boxed{\bigstar{\sf \: {Diagonal = 17 \: cm }}}}$

$\textsf{\underline{Perimeter of the Rectangle :}}$

$\tt{\implies2(length + breadth)}$

$\tt{\implies2(8 + 15)}$

$\tt{\implies16 + 30}$

$\tt{\implies46 \: cm}$

$\large{\boxed{\bigstar{\sf \: {Perimeter \: = 46 \: cm}}}}$

$\therefore$$\text{The Diagonal is 17 cm.}$
$\text{Perimeter is 46 cm}$

Answer 2

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hello...!

$answer$

» The Diagonal is 17 cm.

» Perimeter is 46 cm

» Explanation «

» Given :

Length of the Rectangle = 15 cm

Breadth of the Rectangle = 8 cm
$<font color="blue"><b>$
» To find :

The measure of the diagonal ›

Perimeter of Rectangle

Solution :

Refer the Attachment for better understanding.

In ∆ ACD,

• Base = CD = 15 cm

• Height = AC = 8 cm

• Hypotenuse = AD = x

By Pythagoras Theorem :

(Hypotenuse) ² = (Base)² + (Height)²

» x² = 15²+ 8²

» x² = 225 + 64

» x²=289

» x=17

hypotenuse=17cm

$<font color="green"><b>$★Diagonal=17cm

Perimeter of the Rectangle :

» 2(length+breadth)

» {2(8 + 15)}

» 2(8+15)

» 16+30

» 46cm

★Perimeter=46cm

The Diagonal is 17 cm.

Perimeter is 46 cm
$<font color="violet"><b>$
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