The side of a square is X cm, and the area of the square and the area of a rectangle are equal. If the length and breadth of the rectangle are (2X - 5) cm and (X – 6) cm, respectively, then find perimeter of the rectangle (in cm).
ATQ,
X² = (2X - 5) (X – 6)
X² = 2X² - 12X - 5X + 30
X² - 17X + 30 = 0
X² - 15X – 2X + 30 = 0
X = 15, 2
If X = 2
Breadth of the rectangle = 2 – 6 = -4 cm (can’t possible)
So, X = 15
Length of the rectangle = 2X – 5 = 2(15) – 5
= 25 cm
Breadth of the rectangle = 15 – 6 = 15 – 6 = 9 cm
Required perimeter = 2(25 + 9) = 68 cm
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