The area of a bulletin board is 52 square feet. The length is 3 feet less than4 times the width. Find the length and width

Accepted Solution

Answer:The length of the bulletin board is [tex]13\ ft[/tex]The width of the bulletin board is [tex]4\ ft[/tex]Step-by-step explanation:Letx-----> the length of the bulletin boardy-----> the width of the bulletin boardwe know thatThe area of the rectangle (bulletin board) is equal to[tex]A=xy[/tex]we have[tex]A=52\ ft^{2}[/tex]so[tex]52=xy[/tex] ------> equation A[tex]x=4y-3[/tex] ------> equation Bsubstitute equation B in equation A and solve for y[tex]52=(4y-3)y[/tex] [tex]4y^{2}-3y-52=0[/tex]Using a graphing calculator------> solve the quadratic equationThe solution is [tex]y=4\ ft[/tex]see the attached figureFind the value of x[tex]x=4(4)-3=13\ ft[/tex]