# Solving Quadratic Equations (Word Problems)

- 1Is it possible to make a rectangle that has a perimeter of 40m and an area of 170$m^2$? (Show work and explain.)
- 2Is it possible to make a rectangle that has a perimeter of 80m and an area of 170$m^2$? (Show work and explain.)
- 3A football is kicked and the height, h, in metres of the ball after t seconds is modelled by the function:

$h(t)=-5t^2+25t+1$.

a) How long is the ball in the air? (to the nearest hundredth)

b) How long is the ball above 21m? - 4A rectangular pool that is 5m by 9m is to be surrounded by a deck of equal width all the way around. The area of the deck is equal to the area of the pool. Find the width of the deck to the nearest hundredth.
- 5A rectangular building that is 10m by 12m is to be surrounded by a lawn of equal width all the way around. The total area of the building and the lawn is 200$m^2$. Find the width of the lawn to the nearest hundredth.
- 6The sum of two numbers is 12. Their product is 29. Find the numbers to the nearest hundredth.
- 7The sum of two numbers is 15. Their product is 30. Find the numbers to the nearest hundredth.
- 8The hypotenuse of right triangle is 15cm. the sum of the other two sides is 20cm. Find the length of the other two sides to the nearest hundredth.
- 9The hypotenuse of right triangle is 13cm. the sum of the other two sides is 18cm. Find the length of the other two sides to the nearest hundredth.

$$e=mc^2$$