Answer :
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
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
