Question

the length of a rectangle exceeds its width by 5 M if the width is increased by 1 M and length is decreased by 2m area of a new rectangle is 4 square metres less than the area of the original rectangle . find the dimension of the original rectangle

Answer 1

Hi there !!

Let the width be x metres

Length = x + 5 metres

Area of the original rectangle = length × breadth

= (x + 5)(x)

= x² + 5x metres ______(i)

Given,

If the width is increased by 1 M and length is decreased by 2m,

the new dimensions will be ,

width = x + 1 metres
length = x + 5 - 2 = x + 3 metres

Area of the new rectangle will be

(x + 3)(x) = x² + 3x metres ______(i)


Given,
area of a new rectangle is 4 square metres less than the area of the original rectangle .

So,
a balanced equation can be formed like this :


${x}^{2} + 3x + 4 = {x}^{2} + 5x$

${x}^{2} - {x}^{2} + 3x + 4 = 5x$

Cancelling +x² and -x²,

we have,

$3x + 4 = 5x$

$4 = 5x - 3x$

$4 = 2x$

$x = \frac{4}{2}$
x = 2


So,

Length = x + 5 m = 2 + 5m = 7m
Breadth = x = 2m


Thus,

the length and breadth of the rectangle will be 7m and 2m respectively

Answer 2

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