Quadratic Equations. 6i 



PROBLEMS. 



/. The hypothenuse of a right angled triangle is io,and the 

 excess of the perpendicular over the base is 2. Find the sides of 

 the triangle. 



2. The hypothenuse of a right angled triangle is h, and the 

 excess of the perpendicular over the base is c. Find the sides of 

 the triangle. 



Can e in this problem be assigned any value whatever f 



J. The perimeter of a rectangle is 16 feet, and its area is 15 

 square feet. Find the dimensions of the rectangle. 



4. The perimeter of a rectangle is p feet, and its area is a 

 square feet. Find the dimensions of the rectangle. 



Show, from the result, that the square is the greatest possible 

 rectangle which can be made with a given perimeter. 



5. The sum of the squares of three consecutive odd numbers 

 is 83. Find the numbers. 



What would you say in case the number 56 was given in 

 place of 83? 



Make the problem read so that 56 will be allowable. 



6. The sum of the squares of four consecutive even num- 

 bers is 120. Find the numbers. 



7. If 962 men were drawn up in two squares, and it were 

 found that one square had 18 more ranks than the other, what 

 would be the size of each square ? 



8. A boat's crew row 3)^ miles down a river and back again 

 in I hour and 40 minutes. Supposing the river to have a cur- 

 rent of 2 miles per hour, find the rate at which the crew would 

 row in still water. 



What do you say about tlie negative result ? 



p. A boat's crew row d miles down a river and back again 

 in / hours. Supposing the river to have a current of r miles per 

 hour, find the rate of rowing in still water. 



Show from the result that the problem will always give one 

 positive and one negative value of x for all values of d, t or r. 



