(a).The figure at the below shows a rectangle which has a quarter-circle and a semicircle cut out of it. Find a formula that gives the total perimeter length of this figure in terms of the three letters: “L”, “W” and “ R ”
A: 2L+2W+0.71R
B: 2L+2W-0.71R
C: 2L+2W-0.86R
D: 2L+2W+0.86R

#Q.4(b) Follow the previous diagram find out the Area
A: LW-0.78R^2
B: None of these
C: LW+2.36^2
D: LW-3.14R^2

the forst and 3rd

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240