The perimeter of the quadrilateral is 49 cm. Find the length of the sides. Side one x+4 side two x+9 side three x^2-3x side 4 4x-4

Question

The perimeter of the quadrilateral is 49 cm. Find the length of the sides. Side one x+4 side two x+9 side three x^2-3x side 4 4x-4

Answer 1

The perimeter is the sum of all sides.  Knowing this, set this equation.

 

(x + 4) + (x + 9) + (x² - 3x) + (4x - 4) = 49

 

 

Solve for x.

 

x² + 3x + 9 = 49

 

 

Subtract 49 to both sides of the equation.

 

x² + 3x - 40 = 0

 

 

You now have a quadratic equation.  

 

We can factor the left side of the equation using FOIL.

 

(x + 8)(x - 5) = 0

 

x = -8           and         x = 5

 

 

Since we cannot have negative sides, we accept the solution  x=5.  Plug in this value of x into each algebraic expression to find the four actual sides.