Question

The length and breadth of a rectangle are (2x + 1) cm

and (x + 3) cm, respectively. If the area of the
rectangle is 88 cm^2 ,find:
a. the value of x
b. the perimeter of the rectangle.

Answer 1

Explanation:

Area = 88 sq.cm

length * width = 88

(2x + 1)(x + 3) = 88

2x*(x +3) + 1*(x + 3) = 88

2x*x + 2x*3 + x + 3= 88

2x² + 6x + x + 3 = 88

2x² + 7x + 3 - 88 = 0

2x² + 7x - 85 = 0

2x² - 10x + 17x - 85 = 0

2x(x - 5) + 17(x - 5) =0

(x - 5)(2x + 17 )= 0

x - 5 = 0 {Ignore 2x +17 = 0 as it gives a negative value}

x = 5

b) length = 2x + 1 = 2*5 + 1 = 10 +1 = 11 cm

breadth = x+ 3 = 5 + 3 = 8 cm

Perimeter = 2*(length +breadth}

= 2* (11 + 8)

= 2 * 19

= 38 cm