# Quadratic Equations (Word Problems Part 1)

- 1The width of a rectangle is 1cm shorter than its length. If the area is \(6cm^2\), what are the dimensions?
- 2The length of a rectangle is 4 cm longer than its width. If the area is \(12cm^2\), what are the dimensions?
- 3Two numbers differ by 4. If the numbers are squared and added the result is 40. What are the numbers?
- 4Two numbers differ by 5. If the numbers are squared and added the result is 37. What are the numbers?
- 5A 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!
- 6A 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.
- 7An 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.
- 8The sum of the squares of two consecutive integers is 61. Find the integers.
- 9The sum of the squares of three consecutive even integers is 56. Find the integers.
- 10The sum of the squares of three consecutive odd integers is 83. Find the integers.
- 11The 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.
- 12The 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.

$$e=mc^2$$