The following expressions are the areas of rectangles. Find the possible lengths and breadths of these rectangles.
(i) x² - 6x + 8
(ii) x² - 3x + 2
(iii) x² - 7x + 10
(iv) x² + 19x - 20
(v) x² + 9x + 20

Solution:

(i) x² - 6x + 8

Given, area of the rectangle = x² - 6x + 8

Area of the rectangle = Length × Breadth

Now, find the factors of the given expression:

x² - 6x + 8 = x² - 4x - 2x + 8

= x(x - 4) - 2(x - 4)

= (x - 4)(x - 2)

Hence, the possible length and breadth of the given rectangle are (x - 4) and (x - 2).

(ii) x² - 3x + 2

Given, area of the rectangle = x² - 3x + 2

Area of the rectangle = Length × Breadth

Now, find the factors of the given expression:

x² - 3x + 2 = x² - 2x - 1x + 2

= x(x - 2) - 1(x - 2)

= (x - 2)(x - 1)

Hence, the possible length and breadth of the given rectangle are (x - 2) and (x - 1).

(iii) x² - 7x + 10

Given, area of the rectangle = x² - 7x + 10

Area of the rectangle = Length × Breadth

Now, find the factors of the given expression:

x² - 7x + 10 = x² - 5x - 2x + 10

= x(x - 5) - 2(x - 5)

= (x - 5)(x - 2)

Hence, the possible length and breadth of the given rectangle are (x - 5) and (x - 2).

(iv) x² + 19x - 20

Given, area of the rectangle = x² + 19x - 20

Area of the rectangle = Length × Breadth

Now, find the factors of the given expression:

x² + 19x - 20 = x² + 20x - 1x - 20

= x(x + 20) - 1(x + 20)

= (x + 20)(x - 1)

Hence, the possible length and breadth of the given rectangle are (x + 20) and (x - 1).

(v) x² + 9x + 20

Given, area of the rectangle = x² + 9x + 20

Area of the rectangle = Length × Breadth

Now, find the factors of the given expression:

x² + 9x + 20 = x² + 4x + 5x + 20

= x(x + 4) + 5(x + 4)

= (x + 4)(x + 5)

Hence, the possible length and breadth of the given rectangle are (x + 4) and (x + 5).

✦ Try This:The following expressions are the areas of rectangles, find the possible lengths and breadths of these rectangles: (i) x² + 16x + 39, (ii) x² - 35x + 150, (iii) x² + 21x + 68

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

NCERT Exemplar Class 8 Maths Chapter 7 Problem 93

The following expressions are the areas of rectangles. Find the possible lengths and breadths of these rectangles. (i) x² - 6x + 8, (ii) x² - 3x + 2, (iii) x² - 7x + 10, (iv) x² + 19x - 20, (v) x² + 9x + 20

Summary:

The possible lengths and breadths of the given area of the rectangles (i) x² - 6x + 8, (ii) x² - 3x + 2, (iii) x² - 7x + 10, (iv) x² + 19x - 20 and (v) x² + 9x + 20 are (x - 4) and (x - 2), (x - 2) and (x - 1), (x - 5) and (x - 2), (x + 20) and (x - 1) and (x + 4) and (x + 5)

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