Question

The side of a rectangle are of lengths(2x+1)cm and (3x+1)cm.The area if the rectangles is 117cm^2 .Find x and the perimeter of the rectangle

Answer 1

Hi...☺️

Here is your answer...✌️

GIVEN THAT,

The sides of rectangle are of length
(2x + 1) cm and (3x + 1) cm

★Longer side will be Length and Smaller side will be Breadth of rectangle

=> Length of Rectangle = (3x+1) cm

=> Breadth of Rectangle = (2x+1) cm

And,

Area of Rectangle = 117 cm²

Length×Breadth = 117

(3x+1) × (2x+1) = 117

6x²+3x+2x+1 = 117

6x²+5x+1-117 = 0

6x²+5x-116 = 0

6x²+29x-24x-116 = 0

x(6x+29)-4(6x+29) = 0

(x-4)(6x+29) = 0

=> x = 4 or x = -29/6

=> x = 4
[ Length and breadth cannot be negative ]

=> Length = 3x+1 = 3(4)+1 = 12+1

Length, L = 13 cm

=> Breadth = 2x+1 = 2(4)+1 = 8+1

Breadth, B = 9 cm

Now,

Perimeter of Rectangle = 2(L+B)

= 2(13+9)

= 2×22

= 44 cm

Answer : x = 4 , Perimeter = 44 cm

Answer 2

Hi.

Here is your answer---

____________________

Let the Length and Breadth of a Rectangle be (2x + 1) and (3x + 1) respectively.

Area of the Rectangle = L × B
                         117 = (2x + 1)(3x + 1)
                       6x² + 2x + 3x + 1 = 117
                           6x² + 5x - 116 = 0
                       
                     Splitting the Middle Term,
                       
                     6x² + 29x - 24x - 116 = 0
                     x(6x + 29) - 4(6x + 29) = 0
 
                     By Zero Product Rule,
                      (x - 4)(6x + 29) = 0
             x = 4                              x = -29/6

Rejecting x = -29/6,
[since Length and Breadth of the Rectangle cannot be negative].

Thus, Value of x is 4.

Length = (2x + 1)
            = 2 × 4 + 1
            = 9 cm.

Breadth = (3x + 1)
              = 3 × 4 + 1
              = 13 cm.

For Perimeter of the Rectangle = 2( l + b)
                                                   = 2(9 + 13)
                                                   = 2 × 22
                                                   = 44 cm.

Thus, the Perimeter of the Rectangle be 44 cm.


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Hope it helps.


Have a nice day.