the perimeter of the quadrilateral is 49 centimeters. find the length of each side. when the sides are x+8 x+4 4x-3 & x^2-3x
just solve
x+8 + x+4 + 4x-3 + x^2-3x = 49
To find the length of each side of the quadrilateral, we need to set up an equation using the given information.
The perimeter of a quadrilateral is the sum of all its sides. In this case, the perimeter is given as 49 centimeters. So, we can write the equation:
(x + 8) + (x + 4) + (4x - 3) + (x^2 - 3x) = 49
Let's simplify and solve this equation step by step:
x + 8 + x + 4 + 4x - 3 + x^2 - 3x = 49
Combining like terms, we get:
x^2 + 2x + 4x - 3x + x + 8 + 4 - 3 = 49
Simplifying further:
x^2 + 4x + 9 = 49
Now, let's bring all terms to one side to form a quadratic equation:
x^2 + 4x + 9 - 49 = 0
x^2 + 4x - 40 = 0
To solve this equation, we can factor it or use the quadratic formula. Let's factor it:
(x - 4)(x + 10) = 0
Now, set each factor equal to zero and solve for x:
x - 4 = 0 or x + 10 = 0
x = 4 or x = -10
Since we're dealing with side lengths, we can ignore the negative value of x. So, x = 4.
Now, substitute the value of x into each side expression to find the length of each side:
Side 1: x + 8 = 4 + 8 = 12 centimeters
Side 2: x + 4 = 4 + 4 = 8 centimeters
Side 3: 4x - 3 = 4(4) - 3 = 13 centimeters
Side 4: x^2 - 3x = (4^2) - (3 * 4) = 16 - 12 = 4 centimeters
Therefore, the length of each side of the quadrilateral is 12, 8, 13, and 4 centimeters.