Question

The expression x2 – 6x + 8 is the area of a rectangle. Find the possible length and breadth of the rectangle

Answer 1

$\huge{\boxed{\boxed{\red{\ulcorner{\mid{\overline{\underline{\bf{Answer:-}}}}}\mid}}}}$

Length :-

$\huge\red {l = 2.}$

Breath :-

$\huge\red{B = 4}$

Given :-

Area of rectangle in the form of expression.

so,

Areas of rectangle = Expression.

$\rightarrow l \times b = {x}^{2} - 6x + 8. \\ \\ \rightarrow \: l \times b = {x}^{2} - 4x - 2x + 8. \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = x(x - 4) - 2(x - 4). \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = (x - 2)(x - 4) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\large\pink{Hence,}$

° The long side of rectangle is breadth

so, = 4.

° Similarly Length of rectangle is 2.

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Answer 2

Length of the rectangle = x - 4 & Breadth of the rectangle = x - 2

Given :

The expression x² – 6x + 8 is the area of a rectangle

To find :

The possible length and breadth of the rectangle

Solution :

Step 1 of 2 :

Write down the area of the rectangle.

The expression x² – 6x + 8 is the area of a rectangle

Step 2 of 2 :

Find possible length and breadth of the rectangle

$\sf {x}^{2} - 6x + 8$

$\sf = {x}^{2} - (4 + 2)x + 8$

$\sf = {x}^{2} - 4x - 2x + 8$

$\sf =x(x - 4) - 2(x - 4)$

$\sf =(x - 4) (x - 2)$

x - 2 > x - 4

Hence Length of the rectangle = x - 4

Breadth of the rectangle = x - 2

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