Q:

A rectangular parcel of land has an area of 3,000 ft2. A diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel. What are the dimensions of the land, correct to the nearest foot? ft (smaller value) by ft (larger value)

Accepted Solution

A:
Answer:40 ft × 75 ft Step-by-step explanation:Let x be the one side ( in feet ) of the rectangular parcel,So, the diagonal between opposite corners = ( x + 10 ) feet,Let y be the other side of the rectangle ( adjacent to side x ),The area of the rectangle,A = x × y,According to the question,A = 3000 square ft,[tex]\implies xy = 3000\implies y=\frac{3000}{x}[/tex]∵ In a rectangle,[tex]D^2=a^2+b^2[/tex]Where, a and b are the adjacent side of the rectangle and D is the diagonal,[tex](x+10)^2 = x^2 + y^2[/tex][tex](x+10)^2 = x^2 + \frac{9000000}{x^2}[/tex][tex]x^2(x+10)^2 = x^4 + 9000000[/tex][tex]x^2(x^2+100+20x) = x^4 + 9000000[/tex][tex]x^4+100x^2 + 20x^3 = x^4 + 9000000[/tex][tex]20x^3 + 100x^2 - 9000000=0[/tex][tex]x^3 + 5x^2 - 450000 = 0[/tex]By graphing the equation,We found that,The only real zeros of the equation is at x = 75,Hence, the one side of the rectangle = 75 ft,And, second side = [tex]\frac{3000}{75}[/tex] = 40 ftHence, the dimension of the land is 40 ft × 75 ft