SOLUTION: Over 3700 years ago, in Mesopotamia, math exercises using quadratic equations were written on cuneiform tablets. A cuneiform tablet contains the math exercise: A region consists o

Question 978753: Over 3700 years ago, in Mesopotamia, math exercises using quadratic equations were written on cuneiform tablets. A cuneiform tablet contains the math exercise:
A region consists of two non-overlapping squares of total area 1000. The side of one square is two-thirds of the side of the other square diminished by ten. What are the sides of the two squares.
A. Use the variables x & y to represent the sides of the squares. Then, write a quadratic equation to find the length of a side x of the figure.
B. Use the discriminant to find the number of solutions. How many reasonable solutions are there?
C. Solve the quadratic equation. What are the lengths of both sides of the figure?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
side of smaller square is x
larger y
x^2 + y^2 =1000
but x=(2y/3)-10
(4y^2/9)-(40y/3)+100 +y^2=1000
multiply all by 9
4y^2-120y+900+9y^2=9000
13y^2-120y-8100=0
y= (1/26) {120 +/- sqrt (14400+421200)}
1 reasonable solution.
y=(1/26) {120+660)
y=30 ;; asquare is 30x30; another is 10x10
x=10
y^2=900
x^2=100

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