The front walkway from the street to Pam's house has an area of 250ft^2. Its length is two less than four times its width. Find the length and width of the walkway. Round to the nearest tenth of a foot.

Accepted Solution

Answer:Step-by-step explanation:rectangle is 250ft2. Substituting into the formula for the area of a rectangle, A=length×width, we have250250=(4w−2)(w)=4w2−2wIn the standard form aw2+bw+c=0, this is4w2−2w−250=0Substituting the coefficients a=4, b=−2, and c=−250 into the quadratic formula, we havew=−b±b2−4ac‾‾‾‾‾‾‾‾√2a=−(−2)±(−2)2−4(4)(−250)‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√2(4)=2±4,004‾‾‾‾‾√8There are two solutions for w, which we can evaluate on a calculator.w=≈2+4,004‾‾‾‾‾√88.2andw=≈2−4,004‾‾‾‾‾√8−7.7The width of the rectangle must be positive, so w=8.2. The length is then given by4w−2=4(8.2)−2=30.8Thus, Pam's front walkway has a width of 8.2ft and a length of 30.8ft.