Question

7. The length and the breadth of a rectangle are
(2x + 5) cm and (2x - 1) cm respectively. The area
of the rectangle is three times the area of a square
of sides (x + 1) cm.
(i) Form an equation in x and show that it
reduces to x2 + 2x - 8 = 0.
(ii) Solve the equation x2 + 2x - 8 = 0.
(iii) Find the perimeter of the rectangle.​

Answer 1

Answer:

i.

 

Area of a rectangle is length times breadth.  Area of square is the square of its side length.

 

(2x + 5)(2x - 1) = 3(x + 1)2

 

 

Just expand.

 

4x2 + 8x - 5 = 3(x2 + 2x + 1)

 

4x2 + 8x - 5 = 3x2 + 6x + 3

 

 

Move all terms to the left side.

 

x2 + 2x - 8 = 0

 

 

ii.

 

Solve the quadratic equation using FOIL.

 

 

iii.

 

Plug in the positive x value that you got from part ii into the algebraic expressions for the rectangle from the problem.  Then calculate the perimeter.

 

Perimeter = 2(length) + 2(breadth)

Perimeter = 2(2x + 5) + 2(2x - 1)

Perimeter = 8x + 8

Step-by-step explanation: please mark me as brainliest.

Answer 2

Step-by-step explanation:

the length and the breadth of arectangle are (2× +5)cm and (2× -1cm respectively . the area of the rectangle?