The stadium has a form of a rectangle with two semicircles attached to the short sides. the long side of a rectangle is 2 times longer than the short one. construct the expression for the area of the stadium in terms of x, where x denotes a shorter side of the rectangle

Step-by-step explanation:

The area of a rectangle can be calculated with this formula:

Where "l" is the lenght and "w" is the width.

The area of a semi-circle can be found with this formula:

Where "r" is the radius.

 Let be "x" the shorter side of the rectangle (which is also the diameter of the semi-circle).

Based on the information given in the exercise, you know that:

Since the radius is half the diameter:

Observe the figure attached, which shows the stadium.

The area of the stadium is the sum of the areas of the semi-cirlcles and the rectangle.

Therefore, you can construct the following expression for the area of the stadium is terms of "x":

Simplifying it, you get:

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1