# Quadratic equation - high school - math problems

1. Three parallels The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
2. A rectangle 2 A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
3. Touch x-axis Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
4. Medians in right triangle It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides?
5. Rectangle field The field has a shape of a rectangle having a length of 119 m and a width of 19 m. , How many meters have to shorten its length and increase its width to maintain its area and circumference increased by 24 m?
6. Equation 23 Find value of unknown x in equation: x+3/x+1=5 (problem finding x)
7. Secret treasure Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
8. Reciprocal value How do I calculate a number x that is 9 greater than its reciprocal (1/x)?
9. Completing square Solve the quadratic equation: m2=4m+20 using completing the square method
10. Two cubes The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm2. Calculate the edge length of both cubes.
11. A rectangular patio A rectangular patio measures 20 ft by 30 ft. By adding x feet to the width and x feet to the length, the area is doubled. Find the new dimensions of the patio.
12. Isosceles triangle 9 Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm and altitude is 24cm. Find the area of the isosceles triangle
13. Loan 5 Abdul takes a loan of 200000 from Ali and agrees to repay in number of instalment, each instalment begin with the 2nd exceeding the previous one by 1000, if the first instalment is 500, find how many instalment will be necessary to be wipe out the loan? C
14. Eq2 2 Solve following equation with quadratic members and rational function: (x2+1)/(x-4) + (x2-1)/(x+3) = 23
15. RT sides Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
16. Square side If we enlarge the square side a = 5m, its area will increase by 10,25%. How many percent will the side of the square increase? How many percent will it increase the circumference of the square?
17. Three members GP The sum of three numbers in GP (geometric progression) is 21 and the sum of their squares is 189. Find the numbers.
18. Rectangle There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.
19. Diamond diagonals Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
20. Two resistors Two resistors when they give 25 ohms in series and 4 ohms in parallel what the values of

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