A rectangular parcel of land is 20 ft longer than it is wide. Each diagonal between opposite corners is 100 ft. What are the dimensions of the parcel?
This is an Example in the book but it does not clarify in the text book, Can anybody please show me how to do this?
nevermind I got it
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account paying 13% $
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To solve this problem, we can use the Pythagorean theorem to find the dimensions of the parcel.
Let's assume that the width of the parcel is x ft. Since the length is 20 ft longer than the width, the length of the parcel would be x + 20 ft.
We are also given that the diagonal between opposite corners of the rectangular parcel is 100 ft. Let's call this diagonal D.
According to the Pythagorean theorem, the square of the length of the diagonal (D) is equal to the sum of the squares of the length and width of the rectangle.
So, we have the equation:
D^2 = x^2 + (x + 20)^2
Now, we can substitute the value of D which is 100 ft into the equation:
100^2 = x^2 + (x + 20)^2
Simplifying the equation:
10000 = x^2 + (x^2 + 40x + 400)
Combining like terms:
10000 = 2x^2 + 40x + 400
Rearranging the equation to bring all terms to one side:
2x^2 + 40x + 400 - 10000 = 0
2x^2 + 40x - 9600 = 0
Now, to solve this quadratic equation, we can either factor it (if possible) or use the quadratic formula. In this case, the equation is not easily factorable, so we'll use the quadratic formula.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 2, b = 40, and c = -9600. Plugging in these values in the quadratic formula:
x = (-40 ± √(40^2 - 4 * 2 * -9600)) / (2 * 2)
Simplifying this equation will give us the two possible values of x (the width of the parcel). Once we have the width, we can calculate the length by adding 20 to x.
Please note that to get the exact values, you'll need to solve the equation using a calculator or a computer program capable of handling numerical equations.