**Unit 7 Application Problems**

**Solve application problems using quadratic equations. **

1. A positive real number is 4 less than another. When 8 times the larger is added to the square of the smaller, the result is 96. Find the numbers.

2. A positive real number is 4 less than another. If the sum of the squares of the two numbers is 72, then find the numbers.

3. The area of a rectangle is 46 square inches. If the length is 4 times the width, then find the dimensions of the rectangle. Round off your answers to the nearest hundredth.

4. If the sides of a square measure 9units, then find the length of the diagonal.

5. The area of a rectangle is 20 square inches. If the length is 4 inches less than 6 times the width, then find the dimensions of the rectangle. Round off your answers to the nearest hundredth.