Let's call the original angle x° and the radius of the circle y. The area of the original sector would be x / 360 * πy². The new angle, which is a 40% increase from x, can be represented as 1.4x so the area of the new sector is 1.4x / 360 * πy². Now, to find the corresponding change, we can calculate 1.4x / 360 * πy² ÷ x / 360 * πy² = (1.4x / 360 * πy²) * (360 * πy² / x). 360 * πy² cancels out so we're left with 1.4x / x which becomes 1.4, signifying that the area of the sector increases by 40%.
Substituting the expression for x in equation (1) into equation (2) gives 2(2y + 7) + 2y = 200 .....(3) Equation (3) simplifies to 6y = 186 Therefore y = 31 feet. Substituting the value for y into (1) gives x = 69 feet.
