A semicircle is drawn onto one of the shorter sides of a rectangle. The shorter side of the rectangle measures 4 centimeters. The area of the figure is 41.4 square centimeters. What is the length of the longer side of the rectangle?

Use 3.14 for π.

Enter your answer as decimal in the box.

We are given that :

Using Formulas:

Area of rectangle:

Area of semicircle:

Here, we can know that the figure is composed of one rectangle and one semicircle. Therefore by combining the areas of rectangle and circle and taking the length of rectangle as a variable , we will finds its value ;

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.