Math, asked by hardik53762, 5 months ago

the length of the dignoal of a square is 50cm, find the perimeter of the square​

Answers

Answered by Anonymous
1

perimeter=141.6 cm

Step-by-step explanation:

draw another diagonal from the other end

length of a side= (using pythagoras theorem)

                        =35.4 cm

perimeter=35.4x4

              =141.6 cm

Answered by Aryan0123
5

Given:

  • Length of diagonal of square = 50 cm

To find:

→ Perimeter of square = ?

Solution:

Let the sides of the square be x cm.

\\

(Refer the attachment)

\\

In ∆ABC,

By Pythagoras theorem,

(AC)² = (AB)² + (BC)²

50² = x² + x²

2500 = 2x²

x² = 2500 ÷ 2

\\

 \implies  {x =  \dfrac{ \sqrt{2500} }{ \sqrt{2} }} \\  \\  \implies x =  \dfrac{50}{ \sqrt{2} }  \\  \\ rationalizing \: the \: denominator, \\  \\ x =  \dfrac{50 \times  \sqrt{2} }{ \sqrt{2}  \times  \sqrt{2} }  \\  \\   \implies x =  \dfrac{50 \sqrt{2} }{2}  \\  \\  \therefore \boxed{ \boxed{ \bf{x = 25 \sqrt{2} }}}

\\ \\

Perimeter of a square = 4 × side

Perimeter = 4 × 25√2

\\

Perimeter of square = 100√2 cm

Attachments:

Anonymous: Nice
Anonymous: Perfect :)
Aryan0123: Thank you :-) @itzheartcracer and @BeBrainliest
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