Word Problems to do with Quadratic Equations, Help?

Question

I'm not good AT ALL with word problems. Writing them as equations and all. Anyway, if you could just show me how to write these following word problems as Quadratic Equations, I can finish them myself. Solve them that is. Here are the questions.


Model each problem with a quadratic equation. Then Solve.

17. Find the length of the side of a square with an area of six hundred and twenty five feet squared. (625 ft^2)

18. Find the radius of a circle with an area of one hundred and fifty three, point eight six feet squared. (153.86 ft^2)

Thanks for any help you can offer!

Answer 1

17. Given: Area = 625 ft^2
let x = a side of the square.
Area of a square = length x width = a side x a side = x^2.
therefore, 625 ft^2 = x^2,
x = 25 ft.

18. Given: Area = 153.86 ft^2
let r = radius of the circle.
Area of a circle = pi(r^2).
therefore, 153.86 ft^2 = pi(r^2).
or, r^2 = 153.86 / pi

Answer 2

This problem is not difficult, all you need to do is remember your basic formulas from geometry:

17: If x is the length of the side, then x² = 625 ft²
18: If r is the radius of the circle, then 153.86 ft² = πr²

Answer 3

1) x^2 = 625 ft^2
x = 25

2) Pi*r^2 = 153.86 ft^2
r = 7

Answer 4

Taking length and breadth to be x and y: utilising perimeter 2(x+y)=sixty 8 x+y=34 utilising diagonal with Pythagoras' theorem x^2+y^2=26^2 get one variable out by potential of making it the priority interior the 1st equation x+y=34 y=34-x exchange interior the 2nd equation x^2+(34-x)^2=676 x^2+1156-68x+x^2=676 simplifying it we get 2x^2-68x+480=0 dividing by potential of two we get x^2-34x+240=0 utilising quadratic formulation we get x=24 or 10 if x=24 then y=34-24=10 if x=10 then y=34-10=24 length is 24 cm and breadth is 10 cm ^ represents strengthen to potential of.

Answer 5

17. First lable all of your unknowns: Let x = length of the side of the square. Now remember that a square is a rectangle with all sides being equal.

The area of a square is given by (length of side) X (length of side) or x*x = x^2 = 625

18. The area of a circle is (pi)r^2 where pi is approximately 3.14159. The area of the circle is given to be 153.86
Hence (pi)r^2=153.86

Hope this helps