related to perimeter

Question

an arc SBT ia one quarter of circle with center R and radius 6 cm if the length and width of the diagonal of rectangle ABCR are integers and perimeter of ABCR is 14 find the perimeter of shaded region

Answer 1

Formulas used to solve the math problem:

Perimeter of a rectangle is 2(l + w) l= length, w= width

Length of an arc of a circle is r (theta), r= radius,

theta = angles in radians.

x = multiple

Pythagorean = (a+b+c) x square. a,b = legs , c=hypotenuse

Step 1

Perimeter = 2(l+w) =14

Perimeter = 2(3+4) = 6+8=14

Check the pairs that add up to seven (7): ( 6,1) (2,5) ( 3,4)

(3,4) satisfies the condition that the diagonal is an integer.

For (3,4) = 3 power 2 + 4 power 2 = 9 +16 = 25

Square root of 25 = 5. Diagonal is 5 cm

Step 2

The arc SBT is a quarter of a circle = the angle is pi divided by 2 radians

The radius is 6 cm. 6/2=3 4/2 =2

The length of the arc SBT is r (theta) = 6 x pi/4 = 3pi / 2 cm

Step 3

The perimeter of the shaded region is the sum of the lengths of the arc SBT, the side BC, and the side CT.

BC = 4 cm

CT = 6 - 3 = 3 cm

The perimeter of shaded region = 3 pi divided by

2 + 4 +3 = 3 pi divided by 2 + 7cm

Solution

The perimeter of the shaded region is 3pi/2 + 7 cm

I hope the mathematical calculations (step by step approach) was helpful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H.