Q21. A triangle is 8 cm wider than it is tall. The area is 280 cm2. Find the width (length of the base).

Background

Topic: Solving quadratic equations and geometric applications.

This question tests your ability to set up and solve a quadratic equation based on the formula for the area of a triangle, using a relationship between the base and height.

Key Terms and Formulas

• Area of a triangle:

• Let be the height of the triangle (in cm).

• The base is (since it is 8 cm wider than the height).

• The area is given as $280$ cm2.

Step-by-Step Guidance

1. Write the area formula for the triangle using the given values: .

2. Set the area equal to $280.

3. Multiply both sides by $2.

4. Expand the right side: .

5. Rearrange the equation to standard quadratic form: .

Try solving on your own before revealing the answer!