1. A rectangle has dimensions (3x + 1)cm by (2x+1)cm. Given that the area of the rectangle is 117 cm2, find the value of x, the perimeter of the rectangle.
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Step-by-step explanation:
Given:
dimensions of rectangle are (3x+1) cm by (2x+1)cm
area of rectangle = 117cm2
let l=3x+1, b = 2x+1
sol:
area of rectangle =l*b
= (3x+1)(2x+1)
= 6x2+3x+2x+1
=6x2+5x+1
=6x2-3x-2x+1
= -3x(-2x+1) +1(-2x+1)
=(-2x+1)(-3x+1)
= -2x+1 =0 (or) -3x+1 =0
-2x = -1 -3x = -1
x = -1/-2. x = -1/-3
x = 1/2. x = 1/3
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