Question

Please help it’s urgent please

Answer 1

Perimeter 32 cm achieved.

The lengths of the sides are:

Side one = 12 cm

Side two = 6 cm

Side three = 8 cm

Side four = 6 cm

Absolutely, I’ve been improving my problem-solving abilities in linear equations. Let’s find the length of each side of the quadrilateral.

We are given that the perimeter of the quadrilateral is 32 centimeters. We can set up a system of equations to represent the sides of the quadrilateral, where x represents the length of side one.

Step 1: Set up the equations

We can write the following equations based on the information given in the image:

Side one + side two + side three + side four = perimeter

`x + 8 + x^2 - 2x + x + 2x = 32`

Step 2: Solve the system of equations

Combining like terms and moving terms to the left side, we get:

`x^2 + 2x - 24 = 0`

We can use the quadratic formula to solve for x:

`x = (-b ± √(b^2 - 4ac)) / 2a`

Plugging in the values from the equation, we get:

x = (-2 ± √(2^2 - 4 * 1 * -24)) / 2 * 1

x = (-2 ± √100) / 2

x = 4 or x = -6

Step 3: Find the length of each side

Now that we know the values of x, we can find the length of each side:

Side one = x + 8 = 4 + 8 = 12 cm

Side two = x + 2 = 4 + 2 = 6 cm

Side three =
`x^2 - 2x = 4^2 - 2 * 4 = 8 cm`

Side four = 2x - 2 = 2 * 4 - 2 = 6 cm