Question

An orange triangular warning sign by the side of the road has an area of 300 square centimeters. The base of the sign is 25 centimeters longer than the altitude. Find the measurements of the base and altitude.

Answer 1

The base of the orange triangular warning sign is 40 centimeters, and the altitude is 15 centimeters. We used the area formula for a triangle and solved a quadratic equation to find these measurements.

Step-by-step explanation:

To solve for the base and altitude of the orange triangular warning sign we are given the information that the sign has an area of 300 square centimeters and that the base is 25 centimeters longer than the altitude. We can use the formula for the area of a triangle: Area = 1/2 × base × height.

Let the altitude be 'x' centimeters. Then, the base is 'x + 25' centimeters. Plugging into the formula:

• Area = 1/2 × (x + 25) × x
• 300 cm² = 1/2 × (x + 25) × x

Multiply both sides by 2 to get rid of the fraction:

• 600 cm² = (x + 25) × x

Expand and solve the quadratic equation:

• x² + 25x - 600 = 0
• (x + 40)(x - 15) = 0

So, x is either -40 cm or 15 cm. Since a negative length isn't possible, x must be 15 cm. The altitude is 15 cm, thus the base is 15 cm + 25 cm = 40 cm.

The base of the sign is 40 centimeters and the altitude is 15 centimeters.