Question

The window is comprised of a rectangle and half of an oval (A = abrt). If the total area is 66.84956 sq. ft. and the perimeter is 30.0095 ft (P = 2y + x + √((1/32)(4x^2 + y^2))), what are the values of x and y? (Hint: x and y are integer values.)

A. x = 6, y = 8
B. x = 4, y = 7
C. x = 5, y = 6
D. x = 7, y = 5

Answer 1

To find the values of x and y, set up a system of equations using the given information. The correct answer is x = 7, y = 5.

Step-by-step explanation:

To find the values of x and y, we can set up a system of equations using the given information.

From the area equation, A = abrt, we have:

(1) abrt + πab/2 = 66.84956

From the perimeter equation, P = 2y + x + √((1/32)(4x^2 + y^2)), we have:

(2) 2y + x + √((1/32)(4x^2 + y^2)) = 30.0095

Simplifying equation (1), we have:

(3) abrt + πab/2 = 66.84956

Multiplying equation (3) by 2, we get:

(4) 2abrt + πab = 133.69912

Substituting equation (4) into equation (2), we have:

2y + x + √((1/32)(4x^2 + y^2)) = 30.0095 - πab

Simplifying further:

2y + x + √((1/32)(4x^2 + y^2)) = 30.0095 - 3.14159ab

Since x and y are integer values, we can solve this system of equations using trial and error or a numerical method such as substitution or graphing.

The correct answer option is D. x = 7, y = 5.