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A rectangular parcel of land has an area of 7,000 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?

Sagot :

paulcox
let the dimensions of the sides be x and y
x*y=7000 and sqrt(x^2+y^2)=x+10 (sqrt(x^2+y^2) is how you find the length of the diagonal)
=>y=7000/x
=> sqrt(x^2+(7000/x)^2)=x+10
=> x^2+49,000,000/(x^2)=(x+10)^2
=> x^2+49,000,000/(x^2)=x^2+20x+100
=> x^4+49000000=x^4+20x^3+100x^2
=> 20x^3+100x^2-49000000=0
=> use your calculator
=>x approx = 133
since x*y=7000, y=7000/133
=> y approx = 53

Answer:

Dimension of land = 133.16 ft x 52.57 ft        

Step-by-step explanation:

Area of rectangle = Length x Breadth = LB = 7000 ft²

Diagonal of rectangle is given by

                   [tex]d=\sqrt{L^2+B^2}[/tex]

Given that diagonal between opposite corners is measured to be 10 ft longer than one side of the parcel

That is

                          [tex]\sqrt{L^2+B^2}=B+10[/tex]

Taking square on both sides

                          [tex]L^2+B^2=B^2+20B+100\\\\L^2=20B+100[/tex]

We also have

                   LB = 7000

       [tex]LB=7000\\\\L=\frac{7000}{B}\\\\L^2=\frac{7000^2}{B^2}\\\\20B+100=\frac{7000^2}{B^2}\\\\20B^3+100B^2=49\times 10^6\\\\B^3+5B^2-2450000=0\\\\B=133.16ft\\\\L=\frac{7000}{133.16}=52.57ft[/tex]

Dimension of land = 133.16 ft x 52.57 ft            

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