pre cal

A rectangular parcel of land has an area of 4,000 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?

  1. 👍
  2. 👎
  3. 👁
  1. x^2 + y^2 = diagonal^2 = d^2
    x y = 4000 so y = 4000/x
    d = x+10 so d^2 = x^2 + 20 x + 100

    x^2 + 16*10^6/x^2 = x^2 + 20 x + 100

    16*10^6 = 20 x^3 + 100 x^2

    5 x^3 + 25 x^2 - 4*10^6 = 0

    I do not see an easy way to solve that. Use iteration, x and 5x^3+25 x^2
    x = 10^2 --> 5,250,000 too big
    x = 80 --> 2,720,000 too small
    x = 90 --> 3,847,500 getting close
    x = 92 --> 4,333,568 very close
    x = 91 --> 3,974,880 between 91 and 92
    x = 91.5-> 4,039,610 between 91 and 91.5
    so 91 to nearest foot
    91^2 + y^2 = (91+10))^2
    8281 +y^2 = 10201
    y = 43.8 or 44
    so
    91 by 44

    1. 👍
    2. 👎
  2. let one side be x
    then the diagonal is x+10
    let the third side by y
    x^2 + y^2 = (x+10)^2
    x^2 + y^2 = x^2 + 20x + 100
    y^2 = 20x + 100
    y = √(20x+100)

    so the area of the triangle is half the rectangle area

    (1/2)xy =(1/2)(4000)
    xy = 4000
    x√(20x+100) = 4000
    x^2(20x+100) = 16000000
    20x^3 + 100x^2 - 16000000 = 0
    x^3 + 5x^2 - 800000 = 0

    I must admit that I used Wolfram to solve this
    http://www.wolframalpha.com/input/?i=x%5E3+%2B+5x%5E2+-+800000+%3D+0

    and I got x = 91.1947
    then y = 43.8622
    and the diagonal would be 101.1947


    check:
    area of rectangle = xy = (91.1947)(43.8622) = 4000.00017 (close enough)

    I will let you check if Pythagoras also works out, it does.

    I don't know what method you would have to solve that cubic, since it does not factor, and therefore does not have rational roots.
    Do you know Newton's Method ?

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calc.

    A rectangular plot of land is to be fenced in using two kinds of fencing. Two opposite sides will use heavy-duty fencing selling for $7 a foot, while the remaining two sides will use standard fencing selling for $2 a foot. What

  2. math

    A rectangular field is to be enclosed on four sides with a fence. Fencing costs $8 per foot for two opposite sides, and $2 per foot for the other sides. Find the dimensions of the field of area 900 ft2 that would be the cheapest

  3. Math

    The area of the green square is 9 ft2. The area of the yellow square is 25 ft2. What is the area of the red square (labelled "b" in the diagram)? A) 5 ft2 B) 16 ft2 C) 81 ft2 D) 128 ft2 Oh, "ft2" means squared idkk I did the math

  4. Calculus

    Suppose that you are to make a rectangular box with a square base from two different materials. The material for the top and four sides of the box costs $1/ft2$1/ft2; the material for the base costs $2/ft2$2/ft2. Find the

  1. economics

    Suppose that there are three beachfront parcels of land available for sale in Asilomar and six people who would each like to purchase one parcel. Assume that the parcels are essentially identical and that the minimum selling price

  2. Math help, anyone?

    Find the volume of a square pyramid with a base length of 9 cm and a height of 4 cm. 324 cm3 108 cm3 36 cm3 152 cm3 Find the volume of a cone with a radius of 10 mm and a height of 6 mm. 628 mm3 600 mm3 1,884 mm3 1,254 mm3 Find

  3. Math

    Circumference and Area of a Circle Quiz Part 1 1) Find the Area of the parallelogram (1pt) base:67 hight:52 A)3,302 ft2 B)3,484 ft2****** C)3,752 D)4,020 2)Find the Area of the triangle (1pt) base:2.8cm hight:7.8cm A)21.84 cm2

  4. algebra

    joey and helen are standing in opposite corners of a rectangular field. if the field has dimensions 120ft by 209 ft, how far apart are they? Please help me solve this and lead me through the problem , thank you. :)

  1. Int Algebra

    I need some help. A parcel of land is 6 ft longer than it is wide. The diagonal from one corner to the opposite corner is 174ft. What are the dimensions of the parcel? Thanks for your help.

  2. Geometry B

    A kite has diagonals 5.3 ft and 6 ft. What is the area of the kite? • 5.65 ft² • 15.9 ft² • 31.8 ft² My answer??? • 22.6 ft²

  3. Math

    1. A gardener has 140 feet of fencing to fence in a rectangular vegetable garden. Find the dimensions of the largest area he can fence. Find the possible rectangular area he can enclose. 2. Suppose a farmer has a large piece of

  4. calculus

    A rectangular box is to have a square base and a volume of 50 ft3. The material for the base costs 44¢/ft2, the material for the sides costs 10¢/ft2, and the material for the top costs 26¢/ft2. Letting x denote the length of

You can view more similar questions or ask a new question.