Answer

Correct Answer : a ) 4x – 40

According to the question

Area of the rectangle = x² - 20x + 91

We know that

Area of the rectangle = L × B …….(a)

Where L and B are the length and breadth of the rectangle

⇒ x² - 20x + 91

⇒ x² - 13x - 7x + 91

⇒ x(x - 13) - 7(x + 13)

⇒ (x - 13) × (x - 7)

⇒ Area of the rectangle = (x - 13) × (x - 7) …….. (b)

On Comparing eq(a) and (b) we get

L = (x - 13) and B = (x - 7)

We know that

Perimeter of the rectangle = 2 * (L + B) 

Substituting the value of L and B

⇒Perimeter of the Rectangle = 2 * [(x - 13) + (x - 7)]

⇒ 2 *( x – 13 + x – 7)

⇒ 2 * (2x - 20)

⇒ 4x – 40

Thus, the perimeter of the rectangle =   4x – 40

Hence, (a) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA etc.

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