Chapter 4
Exploring Algebraic Identities
CBSE Class 9
Mathematics Solutions
Educart Mathematics class Class 9 NCERT Exemplar cover
Question:

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.
(A) 25a2−30ab+9b225a^2 - 30ab + 9b^2
(B) 36s2−49t236s^2 - 49t^2

Answer: Verified

(A) Area=25a2−30ab+9b2\text{Area} = 25a^{2} - 30ab + 9b^{2}
=(5a)2−2(5a)(3b)+(3b)2= (5a)^{2} - 2(5a)(3b) + (3b)^{2}
=(5a−3b)2= (5a - 3b)^{2}
Length=breadth=(5a−3b) units\text{Length} = \text{breadth} = (5a - 3b) \text{ units}

(B) Area=36s2−49t2\text{Area} = 36s^2 - 49t^2
=(6s)2−(7t)2= (6s)^2 - (7t)^2
=(6s+7t)(6s−7t)= (6s + 7t)(6s - 7t)
Length=(6s+7t),Breadth=(6s−7t)\text{Length} = (6s + 7t), \text{Breadth} = (6s - 7t)

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