The width of a rectangle is 75% the length of the rectangle. the perimeter of the rectangle is 42 inches. a circle is drawn that
contains all four vertices of this rectangle. if the area of the circle is xπ square inches, then what is the value of x ?
1 answer:
Answer:
x = 56.25
Step-by-step explanation:
The sides of the rectangle are in the ratio 3:4, so those together with the diagonal of the rectangle make a 3-4-5 right triangle. The sum of these adjacent-side ratio units is 3+4 = 7, so the perimeter in ratio units is 2×7 = 14. The actual perimeter is 42 inches, so each ratio unit must stand for ...
(42 in)/(14 units) = 3 in/unit
The diagonal of the rectangle is the diameter of the circle. Its length is 5 units, or ...
(5 units)×(3 in/unit) = 15 inches.
Then the radius is half the diameter, or 7.5 inches.
The area of a circle is given by ...
A = πr² = π(7.5 in)² = 56.25π in²
The value of x is 56.25.
You might be interested in
Answer:
The patient owe $1255.6 .
Step-by-step explanation:
As given
A patient's total surgery charges are $1,278.
The patient must pay the annual deductible of $1,000.
The policy states a 80-20 coinsurance. (i.e 20% of the surgery amount is given by the patient .)
20% is written in the decimal form .
= 0.20
20% of patients surgery cost = 0.20 × $1278
= $ 255.6
Patients owe = Deductible cost + 20% of patients surgery cost
= $1000 + $255.6
= $ 1255.6
Therefore the patient owe $1255.6 .