The diameter of a circle if five times the length of a recatngle. The length of a rectangle is three times the width of the rectangle. All three measurements are integers (in other words, they are not fractions or decimals). The area of the rectangle is 12 square feet. What is the area of the circle? Use 3.14 as pi. Do not round the answer.

Question

Mathematics

Anna Jacobson

13 June, 02:05

The diameter of a circle if five times the length of a recatngle. The length of a rectangle is three times the width of the rectangle. All three measurements are integers (in other words, they are not fractions or decimals). The area of the rectangle is 12 square feet. What is the area of the circle? Use 3.14 as pi. Do not round the answer.

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Answers (1)

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Charlotte Horn · Answer 1

706.5 ft²

Step-by-step explanation:

A. Width of the rectangle

The formula for the area of a rectangle is

A = lw

But, l = 3w, so,

A = (3w) w

= 3w² = 12

w² = 4 Divided each side by 3

w = 2 ft Took the square root of each side

B. Length of rectangle

l = 3w = 6 ft

C. Diameter of circle

d = 5l = 5 * 6 = 30 ft

D. Radius of circle

d = 2r

r = d/2 Divided each side by 2

r = 30/2 = 15 ft

E. Area of circle

A = πr² = 3.14 * 15² = 3.14 * 225 = 706.5 ft²

The area of the circle is 706.5 ft².