Solve the problem.
-The diagonal of the floor of a rectangular office cubicle is 2 ft longer than the length of the cubicle and 5 ft longer than twice the width. Find the dimensions of the cubicle. Round to the nearest tenth, if necessary.
A) width = 4 ft, length = 11 ft
B) width = 9.7 ft, length = 22.4 ft
C) width = 2 ft, length = 9 ft
D) width = 3.9 ft, length = 9.7 ft

Question

Quizplus · Accepted Answer

The diagonal of the floor of a rectangular office cubicle is 2 ft longer than the length of the cubicle and 5 ft longer than twice the width. Let's represent the width of the cubicle as "w" and the length as "l".According to the given information, we can set up the following equations:1. Diagonal = Length + 22. Diagonal = 2 * Width + 5Since the diagonal is the same in both equations, we can equate them:Length + 2 = 2 * Width + 5Now, we can solve for the width "w":Length - 2 * Width = 3Width = (Length - 3) / 2Now, we can substitute this expression for "w" in the first equation:Diagonal = Length + 2Diagonal = Length + 2 * ((Length - 3) / 2)Diagonal = Length + Length - 3Diagonal = 2 * Length - 3We are given that the diagonal is 5 ft longer than twice the width, so we can set up another equation:Diagonal = 2 * Width + 52 * Length - 3 = 2 * ((Length - 3) / 2) + 5Solving for "Length":2 * Length - 3 = Length - 3 + 5Length = 22.4 ftNow, we can substitute this value of "Length" back into our expression for "Width":Width = (Length - 3) / 2Width = (22.4 - 3) / 2Width = 9.7 ftTherefore, the dimensions of the cubicle are:Width = 9.7 ftLength = 22.4 ft

Solve the Problem. -The Diagonal of the Floor of a Rectangular Office Cubicle