Word Problem

Question

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

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