Quadratic Equations (Word Problems Part 1)

1. 1
The width of a rectangle is 1cm shorter than its length. If the area is $6cm^2$, what are the dimensions?
2. 2
The length of a rectangle is 4 cm longer than its width. If the area is $12cm^2$, what are the dimensions?
3. 3
Two numbers differ by 4. If the numbers are squared and added the result is 40. What are the numbers?
4. 4
Two numbers differ by 5. If the numbers are squared and added the result is 37. What are the numbers?
5. 5
A pool measuring 6m by 4m is to be surrounded by a deck that is the same width on all sides. The area of the deck is equal to the area of the pool. Find the width of the deck.  Good test question!
6. 6
A model house measuring 9cm by 5cm is to be surrounded by a lawn that is the same width on all sides. The total area of the model lawn and house is $165cm^2$. Find the width of the lawn.
7. 7
An photograph measuring 10cm by 7cm is to be cropped by removing an equal amount from all sides. If the new area of the photograph is $10 cm^2$, find the new dimensions of the cropped photo.
8. 8
The sum of the squares of two consecutive integers is 61. Find the integers.
9. 9
The sum of the squares of three consecutive even integers is 56. Find the integers.
10. 10
The sum of the squares of three consecutive odd integers is 83. Find the integers.
11. 11
The hypotenuse of a right triangle is 5cm. If the other two sides of the triangle have a sum of 7cm, find the dimensions of the triangle.
12. 12
The hypotenuse of a right triangle is 13cm. If the other two sides of the triangle have a sum of 17cm, find the dimensions of the triangle.

$$e=mc^2$$