Find possible expressions for the length and breadth of each of the following rectangles Class 9

Find possible expressions for the length and breadth of each of the following rectangles Class 9

Question 1.

Find possible expressions for the length and breadth of each of the following rectangles whose areas are given by the following expressions in square units.

i. 25a² - 30ab + 9b²

ii. 36s² - 49t²

Solution:

i. Given,

area = 25a² - 30ab + 9b²

= (5a)² - 2(5a)(3b) + (3b)²

= (5a - 3b)²

...[∵ (A - B)² = A² - 2AB + B²]

= (5a - 3b)(5a - 3b)

Since area of rectangle = length x breadth,

length = 5a - 3b, breadth = 5a - 3b

ii. Given, area = 36s² - 49t²

= (6s)² - (7t)²

= (6s + 7t)(6s - 7t) ...[∵ a² - b² = (a + b)(a - b)]

Since area of rectangle = length × breadth,

length = 6s + 7t and breadth = 6s - 7t

OR

length = 6s - 7t and breadth = 6s + 7t