Question

if one side of a square is increased by 5 metres and the other side is reduced by 5 metres, a rectangle is formed whose perimeter is 30 m. find the side of the original square.​

Answer 1

Step-by-step explanation:

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$\huge{ \maltese{ \bold{ \underline{ \underline{Answer:-}}}}}$

Given :

• One side of a square is increased by 5 m
• Other side is decreased by 5 m
• Then , a rectangle is formed
• Perimeter of rectangular is 30 m

To Find :

• Original side of a square

Formula Used:

• Perimeter of rectangle is 2(l + b)
• Here l refers to the length of rectangle
• And b refers to the breadth of rectangle

Solution :

First , Let us assume that side of the square be x

•°• The sides of rectangle are (x+5) and (x-5)

Here,

• l = x+5
• b = x-5
• Perimeter of rectangle= 30 m

$\boxed{ \frak{ \pink{Perimeter \: \: of \: \: rectangle \: \: = 2(l + b)}}}$

$\longmapsto \bf \: 2(x + 5 + x - 5) = 30$

$\longmapsto \bf \: 2(2x) = 30$

$\longmapsto \bf \: 4x = 30$

$\longmapsto \bf \: x = \frac{30}{4}$

$\longmapsto \bf \: x = 7.5 \: m$

${ \boxed{ \pmb{ \frak{\purple{ \therefore \: \: Original \: \: side \: \: of \: \: a \: \: square \: \: is \: \: 7.5 \: \: m}}}}}$

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Answer 2

let a side of square be : x

now ATQ

one side is decreased by 5 it means (x-5).

and one side is increased by 5 it means (x+5).

therefore

area of square = side×side

(x-5)×(x+5) = x^2-25=0

= x^2=25

= x =√25

= x = 5 units

verify 2(l+b)

so length= x+5 = 5+5 = 10units

and breadth= x-5 = 5-5 = 5 units because 0 cannot be breadth if 0 will be breadth then a rectangle cannot be formed.

2(l+b)= 2×(10+5)= 2×15= 30 units

so therefore side of original square is (5 units)