Question

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The perimeter of a square is 40 cm. find the length of its diagonal.​

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Answer 1

Answer:

P=40 cm Side = 10 cm As S=P/4 (in square) Area = side×side =10×10 =100cm^2 Diagonal => 10^2 +10^2=diagonal^2 (Pythagoras theorem) Diagonal =root (100 +100) Diagonal = root 200

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Answer 2

Step-by-step explanation:

$\large \sf \red{ \underline{ Given : }}$

• The quadrilateral is square.
• Perimeter of square is 40 cm.

$\large \sf \red{ \underline{ To \: Find : }}$

• Length of it's diagonal.

$\large \sf \red{ \underline{ Understanding \: C oncept: }}$

» Firstly here we are given the perimeter of the square. And we need to find the measure of its diagonal. Firstly we will the measure of its each side. Then, we will divide the the square in two triangles. Now, we know that sides of square are equal. So, by using Pythagoras Theorem we can easily find it.

$\large \sf \red{ \underline{ Formula \: used: }}$

$\sf \longmapsto \boxed{ \sf \: \pink{Perimeter _ {(Square)} = 4 \times \: side \: }}$

Pythagoras Theorem states that :

→ h² = p² + b²

Where,

• h = hypotenuse
• p = perpendicular
• b = base

In the case of square, perpendicular and base will be same.

$\large \sf \red{ \underline{ Solution: }}$

Keeping all these things in mind. Let's start solving!

Finding the side,

$\sf \longmapsto \boxed{ \sf \: \pink{Perimeter _ {(Square)} = 4 \times \: side \: }}$

$\sf \longmapsto { \sf \: \pink{40= 4 \times \: side \: }}$

$\sf \longmapsto { \sf \: \pink{ \dfrac{40}{4} =\: side \: }}$

$\sf \longmapsto { \sf \: \pink{ \cancel \dfrac{40}{4} =side \: }}$

$\sf \longmapsto { \sf \: \pink{ 10= \: side \: }}$

So, side is 10 cm.

Using Pythagoras theorem,

$\sf \longrightarrow \: {h}^{2} = {p}^{2} + {b}^{2}$

$\sf \longrightarrow \: {h}^{2} = {10}^{2} + {10}^{2}$

$\sf \longrightarrow \: {h}^{2} = 100+ 100$

$\sf \longrightarrow \: {h}^{2} = 200$

$\sf \longrightarrow \: {h} = \sqrt{200}$

$\bf \longrightarrow \: h = 10\sqrt{2}$

Hence, the measure of the diagonal is 10√2 cm.