The perimeter of the triangle is 41 inches. The perimeter of the rectangle is 66 inches. (Note: Pictures are not drawn to scale) Part A: Write a system of equations to determine x and y.Part B: Solve the system of equations. Use your solution to determine the length and width of the rectangle.

Accepted Solution

Answer:Part A)  The system of equations is equal to[tex]41=4x+7y[/tex][tex]33=(3x+7y)[/tex]Part B) The length is [tex]24\ in[/tex]The width is [tex]9\ in[/tex]Step-by-step explanation:Part A) we know thatThe perimeter of the triangle is equal to the sum of the length of its three sidesIn this problem[tex]41=x+3x+7y[/tex][tex]41=4x+7y[/tex] -----> equation AThe perimeter of rectangle is equal to[tex]P=2(L+W)[/tex]In this problem[tex]66=2(3x+7y)[/tex][tex]33=(3x+7y)[/tex] ------> equation BPart B)Using a graphing toolSolve the system of equationsWe know thatThe intersection point both graphs is the solution of the system of equations[tex]41=4x+7y[/tex][tex]33=(3x+7y)[/tex]The intersection point is [tex](8,9/7)[/tex]see the attached figure[tex]x=8\ in[/tex][tex]y=(9/7)\ in[/tex]step 3Find the length and width of the rectangleThe length is 3x[tex]3*8=24\ in[/tex]The width is 7y[tex]7*(9/7)=9\ in[/tex]